A mirror conjecture for projective bundles
Artur Elezi
提出并证明了光滑复射影流形$X$和$X$上的射影丛$\PP(\oplus L_i)$的量子上同调的$\mathcal D$ -模之间的关系.
We propose, motivate and give evidence for a relation between the $\mathcal D$-modules of the quantum cohomology of a smooth complex projective manifold $X$ and a projective bundle $\PP(\oplus L_i)$ over $X$.
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
Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles
本文研究射影空间上多重射影丛及射影丛相对对称幂的同构分类问题，并进一步刻画了这些对象的自同构群。
In this short article, we determine the bigness of the tangent bundle $T_X$ of the projective bundle $X=\mathbb{P}_C(E)$ associated to a vector bundle $E$ on a smooth projective curve $C$.
We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over $\bP^1$ carries the structure of a projective bundle over some projective space. Furthermore, we construct examples in arbitrary dimension $\ge 3$ of almost homogeneous Fano projective bundles over $\bP^2$ which can be globally deformed to non-almost homogeneous manifolds.
Complements of hyperplane sub-bundles in projective space bundles over the projective line
我们证明了在射影直线上秩为r-1的射影空间丛的充要超平面子丛H的补的抽象代数簇的同构型只依赖于H的r重自交.特别地，它既不依赖于环境丛，也不依赖于具有给定r重自相交的特定的充足超平面子丛。我们的证明利用了意想不到的财产，每一个这样的补充配备了一个非平凡torsor下的向量丛的仿射直线上的双重起源的结构。
On a conjecture by N. Takahashi on log mirror symmetry for the projective plane
根据N.高桥
Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg models
证明了加权射影空间中光滑Fano完全交的Hori-Vafa镜像模型可以解释为Laurent多项式.
The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.
Classical Computation of Number of Lines in Projective Hypersurfaces: Origin of Mirror Transformation
本文讨论了射影超曲面的d=1有理Gromov-Witten不变量的留数整表示的经典推导方法。
Isomorphism of Multiprojective Bundles and Projective Towers
本文研究不同维数光滑射影簇上射影丛的同构问题，证明不同射影空间上的多射影丛除平凡情形外不同构，并给出高度3射影塔顶层簇同构的充要条件。
We show that smooth projective horospherical varieties with nef tangent bundles are rational homogeneous spaces.
Dynamics of Endomorphisms for Projective Bundles on Elliptic Curves
本文通过丛的转移函数研究椭圆曲线上射影丛满射自同态的动力学，证明了其Kawaguchi--Silverman猜想，并将结果推广至具有限生成Mori锥的光滑射影簇上的射影分裂丛。
On the classification of rank 2 almost Fano bundles on projective space
几乎Fano丛是光滑射影簇上的向量丛，它的射影化是几乎Fano簇。本文证明了几乎Fano丛只存在于几乎Fano流形上，并研究了射影空间上的秩2几乎Fano丛。
In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold for jet bundles on projective space in any dimension. We also consider some classes associated to jet bundles in the algebraic K-theory of projective space.
This is a survey article on mirror symmetry and Fourier-Mukai partners of Calabi-Yau threefolds with Picard number one based on recent works by the authors [HoTa1,2,3,4]. For completeness, mirror symmetry and Fourier-Mukai partners of K3 surfaces are also discussed.
Smooth blow up structures on projective bundles
本文在Hartshorne猜想等假设下分类了射影空间上具有光滑爆破结构的射影丛，验证了特定向量丛的相关性质，并得到了同时具有两种结构的簇的新例子。
We study ample vector bundles on smooth projective stacks. In particular, we prove that the tangent bundle for the weighted projective stack $\mathbb{P}(a_0,...,a_n)$ is ample. A result of Mori shows that the only smooth projective varieties with ample vector bundle are isomorphic to $\mathbb{P}^N$ for some $N$. Extending our geometric spaces from varieties to projective stacks, we are able to provide a new example. This leaves the open question of knowing if the only smooth projective stacks are the weighted projective stacks.
This short paper shows that a projective bundle over a smooth variety with a section can be uniquely recovered from the embedding of the section in its second infinitesimal neighborhood within the bundle.
On Serrano's conjecture on Projective bundles
本文针对高维光滑射影簇上的射影丛，考察严格 nef 除子情形下的 Serrano 猜想。
Mirror fibrations and root stacks of weighted projective spaces
我们证明了良构加权射影空间上根栈的轨道Chow环可以自然地看作是奇异簇上函数的Jacobian代数，该奇异簇由其Ginzburg-Landau模型的部分紧化给出.
On projective space bundle with nef normalized tautological divisor
本文研究了相对反标准线丛为nef的射影空间丛的结构。作为应用，我们得到了有限余覆盖下的阿贝尔簇的一个刻画。
We prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli space of strongly parabolic Higgs bundles of rank two or three, with full flags. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank.
Frobenius splitting of projective toric bundles
给出了非奇异环面簇上的环面丛的几个温和条件，在这些条件下环面丛的射影化是Frobenius分裂的。
Automorphisms of Certain Projective Bundles over Toric Varieties
当丛E是线丛的直和时，刻画了单复曲面簇上投射丛P（E）的自同构群。复曲面品种，包括卡拉比-丘m-褶皱和Del Pezzo表面上的完整的交叉点的模量的研究中的应用，表明。
Schwarzenberger bundles on smooth projective varieties
定义了任意光滑射影簇X上的Schwarzenberger丛。本文引入了Steiner丛E在X上的跳跃对的概念，并确定了其跳跃轨迹维数的一个界。对跳对集具有最大维数的Steiner丛进行了完全分类，证明了它们都是Schwarzenberger丛。
Smooth projective toric varieties whose nontrivial nef line bundles are big
对于任意的$n\geq 3$，我们明确地构造了Picard数$\geq 5$的光滑投射环面$n$ -折叠，其中任意非平凡的Nef线丛都是大的.
On globally generated vector bundles on projective spaces II
推广了作者以前的一个结果，对第一陈类为3的射影空间上的整体生成向量丛进行了分类。
Given two equivariant vector bundles over an algebraic GKM manifold with the same equivariant Chern classes, we show that the genus zero equivariant Gromov--Witten theory of their projective bundles are naturally isomorphic.
Linear and Steiner bundles on projective varieties
利用算术Cohen-Macaulay（ACM）簇的Horrocks单子的推广，建立了射影空间和二次超曲面上线性丛和Steiner丛的上同调刻画.我们还研究了ACM簇上丛的线丛分解，并在二次超曲面的情况下刻画了线性同调维数。
Mirror symmetry and open/closed correspondence for the projective line
研究通过镜像对称探讨项目线的开/闭对应关系，建立盘型Gromov-Witten生成函数与toric表面I-函数渐近展开的对应。
Projective manifolds with splitting tangent bundles, I
研究了Kodaira维数不为1和2时，其切丛是子丛的直和的射影三重图的泛覆盖.我们还证明了在任意维上具有分裂切丛的Fano流形的结果。
Hartshorne's conjecture about vector bundles on projective space states that any rank 2 vector bundle on n-dimensional projective space splits as soon as n is at least 7. Klyachko has shown that Hartshorne's conjecture is true when the vector bundles are torus equivariant. Moreover, recent work of Ilten and Süss generalizes Klyachko's work to the case of a smaller rank torus action on projective space. In this note we give a new, direct proof that torus rank 2 bundles split that avoids a description of the category of torus equivariant vector bundles.
We study the equivariantly perturbed mirror Landau-Ginzburg model of the projective line. We show that the Eynard-Orantin recursion on this model encodes all genus all descendants equivariant Gromov-Witten invariants of the projective line. The non-equivariant limit of this result is the Norbury-Scott conjecture, while by taking large radius limit we recover the Bouchard-Marino conjecture on simple Hurwitz numbers.
We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.
A Remark on Projective Embeddings of Varieties with Non-Negative Cotangent Bundles
我们证明了一个关于光滑簇X的投影嵌入的基本的但有点出乎意料的结果，其余切丛是数值有效的。具体地说，我们证明了任何投射嵌入中X的度必须在X的维度上（几乎）指数增长。
Our goal is to study the syzygies of the projective embeddings defined by ample line bundles on a fake projective plane S. The syzygies are studied in terms of the property $N_p$. For various kinds of ample line bundles, we give explicit lower bounds for their powers above which the property $N_p$ is satisfied.
We show that the moduli space of rank three toric vector bundles on smooth projective toric varieties satisfies Murphy's law, that is, every singularity type of finite type arises somewhere on this space.
Mirror symmetry for concavex vector bundles on projective spaces
设$X\subset Y$是光滑的射影流形。设$X$是$\PP^n$上正线性丛的直和$V+$的类属截面的零轨迹。进一步假设正常束$N_{X/Y}$是负线束的直和$V-$。我们证明了$V:=V+\oplus V-$ -扭曲的$\PP^n$的Gromov-Witten理论限制于继承自$Y$的$X$的Gromov-Witten理论。后者可以通过本文证明的镜像定理来计算。
Matrices of linear forms of constant rank from vector bundles on projective spaces
本文利用射影空间上小第一陈类的全局生成向量丛分类，完全刻画了秩不超过六的不可分解常秩线性形式矩阵，并揭示了其与Steiner丛、Drézet丛、刚性齐次向量丛及instanton丛的联系。
The cones of effective cycles on projective bundles over curves
推广Miyaoka等人在除子和曲线情形下的工作，利用Harder-Narasimhan滤子中的数值数据计算复射影曲线上射影丛上任意维数有效圈的锥.最后给出了任意维光滑复射影基上射影丛上的圈的一个应用。
Let $X$ be a toric Del-Pezzo surface and let $Crit(W) \subset (\mathbb{C}^{\ast})^n$ be the solution scheme of the Landau-Ginzburg system of equations. Denote by $X^{\circ}$ the polar variety of $X$. Our aim in this work is to describe a map $L : Crit(W) \rightarrow Fuk_{trop}(X^{\circ})$ whose image under homological mirror symmetry corresponds to a full strongly exceptional collection of line bundles.
Projective bundles of singular plane cubics
分类理论和研究由最小次数的有理曲线所覆盖的射影簇自然会导致奇异有理曲线族的研究。由于家庭的任意奇异曲线是很难处理的，它已被证明在以前的文件中，存在一个部分的奇点的分解，它转换成一束可能严重奇异曲线束节点和尖点平面三次。在分类论感兴趣的情况下，这些丛的全空间显然是投射的。然而，平面三次体的任意丛是全局射影的一般是错误的。由于这个原因，投射性的问题似乎是有趣的，目前的工作给出了一个特征的投射丛。
Convex Fujita numbers: projective bundles
本文研究曲线及阿贝尔簇上曲线半稳定向量丛射影化的有效整体生成性质，属于代数几何领域凸Fujita数相关研究。
On the projective normality of Ulrich bundles on some low-dimensional varieties
本文研究了 Ulrich 向量丛通过其 tautological 线丛的完全线性系嵌入时的射影丛的射影正规性，重点关注定义于曲线、$q=p_g=0$ 曲面及 $2$ 和 $3$ 维超曲面上的 Ulrich 丛。
In this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle. As one of the consequences of the main theorem, we give bounds on very ampleness and projective normality of pluricanonical linear systems on varieties of general type in dimensions three, four and five. These improve known such results.
Characterization theorems for the projective space and vector bundle adjunction
我们考虑光滑射影簇X实际上是射影空间的一些条件。我们还将向量丛的一些结果推广到正特征的情形。我们使用的方法和技术的所谓森理论，特别是研究有理曲线的射影流形。
Quantum cohomology of projective bundles over P^n
本文试图确定射影空间P^n上射影丛的量子上同调。与前面的例子相反，在我们的例子中，相关的模空间通常没有期望的维数。这使得计算更加困难。我们通过使用过度相交理论克服了这个困难。
Vector bundles on projective varieties whose restriction to ample subvarieties split
本文系统地研究了光滑射影簇上的向量丛的分裂问题，该簇对充分向量丛的正则截面的零轨迹的限制使其分裂。首先，我们找到了保证向量丛沿着子簇的分裂意味着它的全局分裂的满度和泛度条件。其次，我们得到了Grassmannian簇和部分旗簇上向量丛的一个简单的分裂准则。
We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.
A Babylonian tower theorem for principal bundles over projective spaces
我们推广了由I。Coanda和G. Trautmann（2006）的方法应用于射影空间上的主$G$ -丛的情形，其中$G$是定义在代数闭域上的线性代数群。在证明的过程中，对这种主$G$ -丛的结构有了新的认识。
Normal bundles of rational curves in projective spaces
我们确定的分裂（同构）类型的一般属0曲线在任何射影空间的1或2个组件的正常丛，以及（有时非平凡的）的方式束变形局部与一般变形的曲线。本文导出了法丛为非一般分裂型的光滑有理曲线除迹线的计数公式。
Identifying quadric bundle structures on complex projective varieties
本文利用某些有理曲线族的几何性质，刻画了在稠密开子集上具有二次丛结构的光滑复射影簇。
Mirror symmetry and quantum cohomology of projective bundles
在以前的文章中，我们证明了光滑簇$X$的量子$\mathcal D$ -模与其上的线丛直和的投影之间的关系，本文证明了当$X$是环面簇中的完全交时的猜想。我们还利用这个猜想证明了由微分算子生成的小量子上同调环$X$的关系提升到投射丛。射影丛的基本上同调关系变形为小量子上同调关系。
Infinitely stably extendable vector bundles on projective spaces
根据Horrocks（1966），射影n-空间上的一个向量丛E稳定地扩张到射影N-空间，N>n，如果在较大的空间上存在一个向量丛，它对较小的向量丛的限制同构于E加上一个线丛的直和。我们证明了对每个N>n，E稳定地扩张到投射N-空间当且仅当E是自由单子（有三项）的上同调。证明使用Coanda和Trautmann（2006）的方法。结合Mohan Kumar，Peterson和Rao（2003）的一个定理，我们得到了射影空间上向量丛的巴比伦塔定理的一个新的有效形式.
Let $U^{'s}_L(n,d)$ be the moduli space of stable vector bundles of rank $n$ with determinant $L$ where $L$ is a fixed line bundle of degree $d$ over a nodal curve $Y$. We prove that the projective Poincare bundle on $Y \times U^{'s}_L(n,d)$ and the projective Picard bundle on $U^{'s}_L(n,d)$ are stable for suitable polarisation. For a nonsingular point $x \in Y$, we show that the restriction of the projective Poincare bundle to $x \times U^{'s}_L(n,d)$ is stable for any polarisation. We prove that for arithmetic genus $g\ge 3$ and for $g=n=2, d$ odd, the Picard group of the moduli space $U'_L…
P1-bundles over projective manifolds of Picard number one each of which admit another smooth morphism of relative dimension one
本文给出了Picard数为1的射影流形上的P1-丛的一个完全分类，其中P1-丛允许另一个相对维数为1的光滑态射。
We prove that the kernel bundle of the evaluation morphism of global sections, namely the syzygy bundle, of a sufficiently ample line bundle on a smooth projective variety is slope stable with respect to any polarization. This settles a conjecture of Ein-Lazarsfeld-Mustopa.
In this article, we study Newton-Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe's estimates used to compute the volume function on these varieties, we compute all Newton-Okounkov bodies with respect to linear flags. Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies.
On Ulrich bundles on projective bundles
本文研究射影丛上Ulrich向量丛的存在性，建立了底簇与射影丛上Ulrich向量丛的关联，并由此在曲线和曲面上的射影丛上证明了其存在性。
Cohomological rank functions and syzygies of projective bundles on abelian varieties
本文利用Jiang–Pareschi上同调秩函数及Caucci–Ito技术研究阿贝尔簇上射影丛的合冲，从而推广并细化了Chiantipalli关于性质$N_p$的结果。
Mirror symmetry and projective geometry of Reye congruences I
通过研究$\mP^4$中Reye同余的Calabi-Yau三重$X$的镜像对称性，我们猜想$X$有一个非平凡的Fourier-Mukai伙伴$Y$ .我们构造$Y$作为在曲线上分支的$\mP^4$中行列式五次曲线的双重覆盖。我们还计算了BPS数的$X$和$Y$（以及相关的卡-丘完全相交$\tilde X_0$）使用镜像对称。
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。