Kelly Jabbusch
In this paper we prove a generalization of a theorem of Schneider, which gives a criterion for a projective surface over the complex numbers to have an ample cotangent bundle. After reviewing different notions of positivity, we introduce a slightly weaker notion of ampleness, which we call quasi-ample, and then are able to extend Schneider's result to higher dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Positivity of the cotangent sheaf of singular Calabi-Yau varieties
该研究推广了前人成果，证明正规射影klt Calabi-Yau簇及不可约全纯辛簇的切层与自反余切层非伪有效，并给出了余维2带奇性的低维Calabi-Yau簇实例。
Generalising a classical theorem by Ueno, we prove structure results for manifolds with nef or semiample cotangent bundle.
Remarks on the positivity of the cotangent bundle of a K3 surface
本文利用 Bayer-Macrì 的结果计算了光滑射影 K3 曲面射影化余切丛的伪有效锥与 nef 锥，并构造光滑曲线显式族证明余切丛限制非半稳定，从而给出 Campana-Peternell 问题的反例。
We construct examples to show that having nef cotangent bundle is not preserved under finite ramified covers. Our examples also show that a projective manifold with Stein universal cover may not have nef cotangent bundle, disproving a conjecture of Liu-Maxim-Wang.
The aim of this work is to construct examples of pairs whose logarithmic cotangent bundles have strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum of at least n general sufficiently ample hypersurfaces.
In this paper we study the positivity of the cotangent bundle of projective manifolds. We conjecture that the cotangent bundle is pseudoeffective if and only the manifold has non-zero symmetric differentials. We confirm this conjecture for most projective surfaces that are not of general type.
Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
A theorem of the first author states that the cotangent bundle of the type $A$ Grassmannian variety can be embedded as an open subset of a smooth Schubert variety in a two-step affine partial flag variety. We extend this result to cotangent bundles of cominuscule generalized Grassmannians of arbitrary Lie type.
Remarks on the positivity of the cotangent bundle of an Enriques surface
本文研究了Enriques曲面余切包在特定曲线限制下的半稳定性，并给出了破坏其稳定的曲线族构造。
We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample cotangent bundle. We discuss the conjecture that the analogous statement should hold in the projective space. Finally, we present a construction due to Bogomolov of varieties with ample cotangent bundle as linear sections of a product of varieties with big cotangent bundle.
We give a new criterion for when a resolution of a surface of general type with canonical singularities has big cotangent bundle and a new lower bound for the values of $d$ for which there is a surface with big cotangent bundle that is deformation equivalent to a smooth hypersurface in $\mathbb{P}^3$ of degree $d$.
We show that there is an affine Schubert variety in the infinite dimensional partial Flag variety (associated to the two- step parabolic subgroup of the Kac-Moody group {\hat SL(n)}, corresponding to omitting α_0,α_d) which is a natural compactification of the cotangent bundle to the Grassmann variety.
We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow (almost) exponentially in the dimension of X.
A non-vanishing conjecture for cotangent bundles on elliptic surfaces
本文证明了等平凡椭圆曲面上余切丛的非消失猜想，并结合已有结果完全解决了Kodaira维数至多1的曲面上的该问题。
In this paper we study the problem of density in (1,3] for the Chern ratio of surfaces with ample cotangent bundle. In particular we prove density in (1,2) by constructing a family of complete intersection surfaces in a product of varieties with big cotangent bundle. We also analyse the case of complete intersections in a product of curves of genus at least 2.
We study the connection between the generation of a fat point scheme supported at general points in the plane and the behaviour of the cotangent bundle with respect to some rational curves particularly relevant for the scheme. We put forward two conjectures, giving examples and partial results in support of them.
In this paper, we prove that a smooth projective globally $F$-split variety with numerically flat tangent bundle is an étale quotient of an ordinary abelian variety. We also show its logarithmic analog, which contains a characterization of toric varieties. We further prove that, without assumption of global $F$-splitting, a smooth projective separably rationally connected variety of arbitrary characteristic with numerically flat log cotangent bundle is a toric variety.
Consider a projective manifold X and suppose that some wedge power of the cotangent bundle contains a subsheaf whose determinant bundle has maximal Kodaira dimension. Then we prove that X is of general type. More generally we compute the Kodaira dimension if the determinant bundle has sufficiently large Kodaira dimension. This is based on the study of the determinant bundle of a quotient of the cotangent bundle of a non-uniruled manifold: this bundle is always pseudo-effective. We apply this to study the universal cover of a projective manifold. Finally we prove the following: if the canonical…
In this paper, we show that there is a natural Lagrangian fibration structure on the map $Φ$ from the cotangent bundle of a del Pezzo surface $X$ of degree 4 to $\mathbb C^2$. Moreover, we describe explicitly all level surfaces of the above natural map $Φ$.
Let $X$ be a Hyperkähler manifold, and let $H$ be an ample divisor on $X$. We give a lower bound in terms of the Beauville-Bogomolov form $q(H)$ for the twisted cotangent bundle $Ω_X \otimes H$ to be pseudoeffective. If $X$ is deformation equivalent to the Hilbert scheme of a K3 surface the lower bound can be written down explicitly and we study its optimality.
In this article we consider log canonical pairs which are log-smooth. If the corresponding canonical bundle is pseudo-effective, then we show that any quotient of the orbifold cotangent bundle of the pair has a pseudo-effective determinant. One of the new ingredients in the proof is a generalization of the Bogomolov-McQuillan algebraicity criterion in the context of holomorphic foliations whose minimal slope with respect to a movable class is positive.
We consider a complex smooth projective variety equipped with an action of an algebraic torus with a finite number of fixed points. We compare the motivic Chern classes of Białynicki-Birula cells with the $K$-theoretic stable envelopes of cotangent bundle. We prove that under certain geometric assumptions satisfied e.g. by homogenous spaces these two notions coincide up to normalization.
Proven by A. Parshin and S. Arakelov in the early 70's, Shafaverich hyperbolicity conjecture states that a family of curves of genus $g\ge2$ parametrized by a non hyperbolic curve (\emph{i.e.} isomorphic to $\mathbb{P}^1$, $\mathbb{C}$, $\mathbb{C}^*$ or an elliptic curve) has to be isotrivial : the moduli of smooth fibres are constant. In higher dimensions, Viehweg's works on moduli of canonically polarized manifolds led him to generalize this statement in the following way: if a family of canonically polarized manifolds (parametrized by a quasi-projective base) has maximal variation, the bas…
For a regular scheme and a prime number $p$, we define the FW-cotangent bundle as a vector bundle on the closed subscheme defined by $p=0$, under a certain finiteness condition. For a constructible complex on the etale site of the scheme, we introduce the condition to be micro-supported on a closed conical subset in the FW-cotangent bundle. At the end of the article, we compute the singular supports in some cases.
A scheme of computing $χ(\mbar_{1,n}, L_1^{\otimes d_1}\otimes ... \otimes L_n^{\otimes d_n})$ is given. Here $\mbar_{1,n}$ is the moduli space of $n$-pointed stable curves of genus one and $L_i$ are the universal cotangent line bundles defined by $x_i^*(ω_{C/M})$, where $C \to \mbar_{1,n}$ is the universal curve, $ω_{C/M}$ the relative dualizing sheaf and $x_i$ the marked point. This work is a sequel to \cite{YL1}.
In this paper, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety, under suitable conditions. In particular when the Picard number is one, we obtain results for any log Del Pezzo surface, log Fano threefolds, and for log Fano $n$-folds of dimension $n\leq 6$.
We prove that a general complete intersection of dimension $n$, codimension $c$ and type $d_1, \dots, d_c$ in $\mathbb{P}^N$ has ample cotangent bundle if $c \geq 2n-2$ and the $d_i$'s are all greater than a bound that is $O(1)$ in $N$ and quadratic in $n$. This degree bound substantially improves the currently best-known super-exponential bound in $N$ by Deng, although our result does not address the case $n \leq c < 2n-2$.
It is known that the cotangent bundle $Ω_Y$ of an irreducible Hermitian symmetric space $Y$ of compact type is stable. Except for a few obvious exceptions, we show that if $X \subset Y$ is a complete intersection such that $Pic(Y) \to Pic(X)$ is surjective, then the restriction $Ω_{Y|X}$ is stable. We then address some cases where the Picard group increases by restriction.
Stability of the Cotangent Bundle on Surfaces with Ample Canonical Class
本文研究K3曲面及具有丰富典范类的曲面上余切丛的Bridgeland稳定性，找到了阈值$t_0$使得余切丛在$t>t_0$时半稳定，并探讨了伪射影平面和伪二次曲面等特例。
The cotangent bundle of K3 surfaces of degree two
研究二次度极一般极化K3曲面余切丛的射影化，揭示其丰富几何，并描述与三次曲面双切曲面类似的曲面D_S。
We give an effective algorithm to compute the Euler characteristics $χ(\mbar_{1,n}, \otimes_{i=1}^n L_i^{d_i})$. In addition, we give a simple proof of Pandharipande's vanishing theorem $H^j (\mbar_{0,n}, \otimes_{i=1}^n L_i^{d_i})=0$ for $j \ge 1, d_i \ge0$.
In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular to obtain convenient (and completely explicit) descriptions of cohomology of twisted symmetric powers of cotangent bundles of complete intersections, which are easily implemented on computer. We then provide several applications. First, we recover the known vanishing theorems on the subject, and show that they are optimal via some non-vanishing theorems. Then, we study the symmetric algebra of global sections of symme…
Let $K$ be the function field of a smooth curve over an algebraically closed field $k$. Let $X$ be a scheme, which is smooth and projective over $K$. Suppose that the cotangent bundle $Ω_{X/K}$ is ample. Let $R:={\rm Zar}(X)(K)\cap X)$ be the Zariski closure of the set of all $K$-rational points of $X$, endowed with its reduced induced structure. We prove that there is a projective variety $X_0$ over $k$ and a finite and surjective $K^{\rm sep}$-morphism $X_{0,K^{\rm sep}}\to R_{K^{\rm sep}}$, which is birational when ${\rm char}(K)=0$.
Let $P$ be a parabolic subgroup in $G=SL_n(\mathbf k)$, for $\mathbf k$ an algebraically closed field. We show that there is a $G$-stable closed subvariety of an affine Schubert variety in an affine partial flag variety which is a natural compactification of the cotangent bundle $T^*G/P$. Restricting this identification to the conormal variety $N^*X(w)$ of a Schubert divisor $X(w)$ in $G/P$, we show that there is a compactification of $N^*X(w)$ as an affine Schubert variety. It follows that $N^*X(w)$ is normal, Cohen-Macaulay, and Frobenius split.
Surfaces of general type with positive second Segre number are known to have big cotangent bundle. We give a new criterion ensuring that a surface of general type with canonical singularities has a minimal resolution with big cotangent bundle. This provides many examples of surfaces with negative second Segre number and big cotangent bundle.
In this paper, we study a variation of a conjecture of Debarre on positivity of cotangent bundles of complete intersections. We establish the ampleness of Schur powers of cotangent bundles of generic complete intersections in projective manifolds, with high enough explicit codimension and multi-degrees. Our approach is naturally formulated in terms of flag bundles and allows one to reach the optimal codimension. On complex manifolds, this ampleness property implies intermediate hyperbolic properties. We give a natural application of our main result in this context.
We use the G-invariant non-degenerate form on the Steinberg module to Frobenius split the cotangent bundle of a flag variety in good prime characteristics. This was previously only known for the general linear group. Applications are a vanishing theorem for pull back of line bundles to the cotangent bundle (proved for the classical groups and G_2 by Andersen and Jantzen and in characteristic zero by B. Broer (for all groups)), normality and rational singularities for the subregular nilpotent variety and good filtrations of the global sections of pull backs of line bundles to the cotangent bund…
We describe the possible restrictions of the cotangent bundle Ω_{\PP^N} to an elliptic curve C \subset \PP^N. We apply this in positive characteristic to the computation of the Hilbert-Kunz function of a homogeneous R_+-primary ideal I \subset R in the graded section ring R = \bigoplus_{n \in \NN} Γ(C, Ø(n)).
We show that there is a ${SL_n}$-stable closed subset of an affine Schubert variety in the infinite dimensional Flag variety (associated to the Kac-Moody group ${\widehat{SL_n}}$) which is a natural compactification of the cotangent bundle to the finite-dimensional Flag variety ${SL_n/B}$.
Let A be an elliptic curve, and let $V_A$ be the Serre vector bundle on A. A famous example of Demailly-Peternell-Schneider shows that the tautological class of $V_A$ contains a unique closed positive current. In this survey we start by generalising this statement to arbitrary compact Kähler manifolds. We then give an application to abelian fibrations $X \rightarrow Y$ where the total space X has pseudoeffective cotangent bundle and raise some questions about nonvanishing properties of these bundles.
We examine the structure of the cotangent bundle $T^{*}X$ of an algebraic variety $X$ acted on by a reductive group $G$ from the viewpoint of equivariant symplectic geometry. In particular, we construct an equivariant symplectic covering of $T^{*}X$ by the cotangent bundle of a certain variety of horospheres in $X$, and integrate the invariant collective motion on $T^{*}X$. These results are based on a "local structure theorem" describing the action of a certain parabolic in $G$ on an open subset of $X$, which is interesting by itself.
In this short note, we will gives several remarks on rational points of varieties whose cotangent bundles are generated by global sections. For example, we will show that if the sheaf of differentials of a projective variety X over a number field k is ample and generated by global sections, then the set of k-rational points of X is finite.
A canonical hyperkaehler metric on the total space $T^*M$ of a cotangent bundle to a complex manifold $M$ has been constructed recently by the author (see alg-geom/9710026). This paper presents the results of alg-geom/9710026 in a streamlined and simplified form. The only new result is an explicit formula obtained for the case when $M$ is an Hermitian symmetric space.
Tangent, cotangent, normal and conormal bundles are almost never instanton bundles
本文给出了特征无关的初等证明，表明切丛、余切丛、法丛和余法丛几乎从不是 instanton bundle，推广了复数域上关于 Ulrich bundle 的已有结果，并探讨了余切丛和切丛扭转的类似情况。
We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.
Let $P$ be a parabolic subgroup in $SL_n(\mathbb C)$. We show that there is a $SL_n(\mathbb C)$-stable closed subvariety of an affine Schubert variety in an infinite dimensional partial Flag variety (associated to the Kac-Moody group ${\widehat{SL_n}(\mathbb C)}$) which is a natural compactification of the cotangent bundle to $SL_n(\mathbb C)/P$. As a consequence, we recover the Springer resolution for any orbit closure inside the variety of nilpotent matrices.
In this paper, we investigate the structure of the convergent quantization of the 1-shifted cotangent bundle $S$ of a smooth scheme $X$ over a perfect field of positive characteristic. The quantization is an $E_2$-algebra over the Frobenius twist $S'$ of the 1-shifted cotangent bundle which restricted to the zero section $X'\rightarrow S'$ is weakly $E_2$-Morita equivalent to the structure sheaf $\mathscr O_{X'}$ of the Frobenius twist $X'$ of $X$. Explicitly, we show that the $(\infty,2)$-category of coherent (left-)modules over $\mathscr O_{X'}$ is equivalent to the full subcategory of the $…
We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent bundle. This description is based on the hypergeometric integral representations for solutions of the equivariant quantum differential equation. We identify the space of solutions with the space of the equivariant K-theory algebra of the cotangent bundle. In particular, we show that for any element of the monodromy group, all entries of its matrix in the standard basis of the equivariant K-theory algebra of the cotang…
We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a gl_n partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.
Toric hyperk{ä}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperk{ä}her manifolds as GIT quotients, we first establish geometrical criteria for the semi-stable points. Then based on these criteria, we show that the cotangent bundles of compact toric varieties in the core of toric hyperk{ä}hler manifold are sufficient to glue the desired toric hyperk{ä}hler manifold.
Following the program of algebraic Frobenius splitting begun by Kumar and Littelmann, we use representation-theoretic techniques to construct a Frobenius splitting of the cotangent bundle of the flag variety of a semisimple algebraic group over an algebraically closed field of positive characteristic. We also show that this splitting is the same as one of the splittings constructed by Kumar, Lauritzen, and Thomsen.
Using compactifications in the logarithmic cotangent bundle, we obtain a formula for the Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement. This generalizes earlier results of Aluffi and Wu-Zhou. The first application of our formula is a geometric description of Chern-Mather classes of an arbitrary very affine variety, generalizing earlier results of Huh which held under the smooth and schon assumptions. As the second application, we confirm an involution formula relating sectional maximum likelihood (ML) degrees and ML bidegrees, whi…
Shifted cotangent bundles, symplectic groupoids and deformation to the normal cone
本文研究移位辛结构在相对情形和非几何堆叠中的推广，提出移位余切丛和AKSZ程序，并定义移位拉格朗日映射的变形到正则锥。
On semiample vector bundles and parallelizable compact complex manifolds
该研究利用全纯对称微分刻画可平行化紧复流形及其商空间，证明了不同半充足性余切丛下小平维数为0的紧复流形的结构，还得到相关基本群性质并提出猜想。
The cotangent bundle of $G/U_P$ and Kostant-Whittaker descent
本文证明了约化群抛物仿射底空间余切丛的函数代数同构于万有中心化子作用下的不变函数子代数，并推广到模情形及部分 Whittaker 余切丛，从而证明 Devalapurkar 猜想。
Birationally equivalent Landau-Ginzburg models on cotangent bundles and adjoint orbits
研究了最小半单伴随轨道上的李势能与庞特里亚金势能的双有理等价性，并探讨了变形家族中朗之万-金斯堡模型的变形对镜像的影响。
We conjecture the equality of the numerical and Kodaira dimensions $ν_1^*(X)$ and $κ_1^*(X)$ for the cotangent bundle of compact Kähler manifolds $X$, generalising the classical case of the canonical bundle. We show or reduce it to the classical case of the canonical bundle for some peculiar manifolds: among them, the rationally connected ones, or resolutions of varieties with klt singularities and trivial first Chern class, in which case we show that $ν_1^*(X)=κ_1^*(X)=q'(X)-dim(X)$, where $q'(X)$ is the maximal irregularity of a finite étale cover of $X$. The proof rests on the Beauville-Bog…
Let $G$ denote a complex semisimple linear algebraic group, $P$ a parabolic subgroup of $G$ and $\mathcal{P}=G/P$. We identify the quantum multiplication by divisors in $T^*\mathcal{P}$ in terms of stable basis, which is introduced by Maulik and Okounkov. Using this and the restriction formula for stable basis, we show that the $G\times\mathbb{C}^*$-equivariant quantum multiplication formula in $T^*\mathcal{P}$ is conjugate to the conjectured formula by Braverman.
Abundance of affine algebraic structures on stabilized cotangent bundles of surfaces
该研究针对亏格$g\geq2$的定向曲面稳定余切丛，构造了不可数多个互不同构且与$T^\ast\Sigma_g\times\mathbb{C}$ Stein形变等价的光滑仿射三维流形，其族由$(6g-7)$维复orbifold参数化，解答了Ivan Smith的问题。
We interpret the equivariant cohomology algebra H^*_{GL_n\times\C^*}(T^*F_λ;\C) of the cotangent bundle of a partial flag variety F_λparametrizing chains of subspaces 0=F_0\subset F_1\subset\dots\subset F_N =\C^n, \dim F_i/F_{i-1}=λ_i, as the Yangian Bethe algebra of the gl_N-weight subspace of a gl_N Yangian module. Under this identification the dynamical connection of [TV1] turns into the quantum connection of [BMO] and [MO]. As a result of this identification we describe the algebra of quantum multiplication on H^*_{GL_n\times\C^*}(T^*F_λ;\C) as the algebra of functions on fibers of a discr…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。