Sebastián Reyes-Carocca
Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding Jacobian varieties. We also give a classification and description of the one-dimensional families of compact Riemann surfaces as before.
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
Pluricanonical systems of projective 3-folds of general type
证明了对任意正整数$m\geq 18(2^{9}\cdot 3^{7})!$和任意复数上的一般型光滑3重射影X，$\mid mK_{X}\mid$给出从X到射影空间的双有理有理映射.
The Cohomology of Reflexive Sheaves on Smooth Projective 3-folds
研究了光滑射影三重上自反秩2层的上同调。给出了自反层的模空间的应用。
Simple Models of Quasihomogeneous Projective 3-Folds
设X是关于线性代数群的作用拟齐次的3重射影复形。我们证明了X是SL_2/G的紧化，G是离散子群，或者X可以等变变换到三维射影空间，二次曲面Q_3，或者变换到某些结构非常简单的拟齐次丛。
Relatively Minimal Quasihomogeneous Projective 3-Folds
本文在自同构群不可解的假设下，对相对极小的三维拟齐次复射影簇进行了分类。通过相对极小，我们理解簇X至多具有Q-阶乘终端奇点，并且允许X到Y的极值收缩，其中dim Y <3。
In this paper, we will construct new examples of derived equivalent Calabi--Yau 3-folds with Picard number greater than one. We also study their mirror Calabi--Yau manifolds and find that they are given by Schoen's fiber products of suitable rational elliptic modular surfaces.
In two recent papers, we described some Siegel modular threefolds which admit a weak Calabi--Yau model. Not all of them admit a {\it projective} model. The purpose of this paper is to exhibit criterions for the projectivity, to treat several examples, and to compute their Hodge numbers.
On The Log Sarkisov Program For Foliations On Projective 3-Folds
本文证明了具有适当奇点的投影三重曲面上协秩为一的叶状结构的Sarkisov程序，并展示了两个具有秩一叶状结构的叶状Mori纤维空间之间的弱化理性刚性。
In this paper we study pluricanonical maps of minimal projective 3-folds of general type with geometric genus $1$, $2$ and $3$. We go in the direction pioneered by Enriques and Bombieri, and other authors, pinning down, for low projective genus, a finite list of exceptions to the birationality of some pluricanonical map. In particular, apart from a finite list of weighted baskets, we prove the birationality of $φ_{16}$, $φ_{6}$ and $φ_{5}$ respectively.
On the pluricanonical map of projective 3-folds of general type with $P_3 \geq 2$
该数学代数几何领域的研究证明，第三多亏格不小于2的光滑一般型射影三维簇，当m不小于14时多典范映射φ_m双有理，且该下界最优。
Let $k$ be an algebraically closed field of characteristic $p > 0$. Let $X$ be an irreducible smooth projective curve of genus $g$ over $k$. Fix an integer $n \geq 2$, and let $S^n(X)$ be the $n$-fold symmetric product of $X$. In this article we find the $S$-fundamental group scheme and Nori's fundamental group scheme of $S^n(X)$.
Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally generated.
Projective 3-folds of general type with X=1
Iano-Fletcher和Reid在大约20年前发现了具有$χ(\mathcal {O})=1$的一般类型的3-折叠的许多例子。Iano-Fletcher曾用$χ(\mathcal {O}_X)=1$证明了一般型的所有极小3重$X$的$P_{12}(X)\ge 1$和$P_{24}(X)\ge 2$。本文对Fletcher方法进行了改进。我们的主要结果是，$ϕ_m$是双有理数到它的图像上的所有$m\ge 54$。为了证明这一点，我们建立了一般3重的双合理性的一般理论，改进了已知的结果。此外，我们将显示所有$m\geq 14$和$P_{18}\geq 3$的$P_m\geq 1$。
On the pluricanonical map and the canonical volume of projective 4-folds of general type
本文研究了一般型非奇异射影4-重的多重典范映射双有理性的有效界及典范体积下界，证明了当m≥76m0+77时φ_m双有理，并给出Vol(V)的下界，改进了Meng Chen的早期结果。
Moduli of Reflexive Sheaves on Smooth Projective 3-folds
我们计算了无挠秩2层的模空间在对应于稳定自反层的点处的期望维数，并给出了一类光滑射影三重层上存在完美切阻复形的条件;这类光滑射影三重层包括Fano和Calabi-Yau三重层。我们还探讨了自反秩2层的模空间和曲线的希尔伯特方案之间的局部和全局关系。
Conifold Transitions for Complete Intersection Calabi-Yau 3-folds in Products of Projective Spaces
本文证明了射影空间乘积上的通用完全相交 Calabi-Yau 3-流形可经历 conifold 转变成为 S^{3} × S^{3} 的连通和，从而在其上构造出具有平凡典范丛的复结构，推广了前人使用五次多项式的方法。
3-fold symmetric products of curves as hyperbolic hypersurfaces in $\Proj^4$
我们构造了射影四维空间中Kobayashi双曲超曲面的新例子。它们是亏格至少为7的一般曲线的三重对称乘积的一般投影，光滑地嵌入射影7-空间。
Ample line bundles on certain toric fibered 3-folds
本文研究具有到射影直线的满射环面等变态射的射影非奇异环面3维流形，证明了其上的丰富线丛总是正规生成。
We supply a detailed proof of the result by P.S. Green and T. H$\ddot{\text{u}}$bsch that all complete intersection Calabi--Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the standard web). We also introduce a subclass of small transitions which we call primitive small transitions and study such subclass. More precisely, given a small projective resolution $π: \widehat{X} \rightarrow X$ of a Calabi--Yau 3-fold $X$, we show that if the natural closed immersion $Def(\widehat{X}) \hookrightarrow Def(X)$ is an isomorphism then $X$ has on…
We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection of H . In particular it depends neither on the ambient bundle nor on a particular ample hyperplane sub-bundle with given r-fold self-intersection. Our proof exploits the unexpected property that every such complement comes equipped with the structure of a non trivial torsor under a vector bundle on the affine line with a double origin.
As an application of universal polynomials for local and multi-singularities of maps, we revisit classical enumerative formulae of Salmon-Cayley-Zeuthen for projective surfaces and analogous formulae of Segre-(B.)Severi-Roth for projective $3$-folds. In particular, several examples of actual computation are given using universal polynomials for computing weighted Euler characteristics of singularity loci.
On the genus of a curve in a projective $3$-fold
本文在 Liu 的结果基础上，改进了 Castelnuovo 对曲线算术亏约的界，并在 Calabi-Yau 情况下推进了关于 Gopakumar-Vafa 不变量消失的猜想。
We address the following question: what are the cardinalities of maximal finite families of pairwise incident planes in a complex projective space? One proves easily that the span of the planes has dimension 5 or 6. Up to projectivities there is one such family spanning a 6-dimensional projective space - this is an elementary result. Maximal finite families of pairwise incident planes in a 5-dimensional projective space are considerably more misterious: they are linked to certain special (EPW) sextic hypersurfaces which have a non-trivial double cover, generically a hyperkaehler 4-fold. We pro…
Let $(X, A)$ be a nonsingular polarized toric 3-fold. We show that if the adjoint bundle of $A$ has no glabal section, then all ample line bundles on $X$ are normally generated. Even if the adjoint bundle is effective, if it is not big, then it is shown the normal generation. In particular, we show that all ample line bundles on a nonsingular toric Fano 3-fold are normally generated.
Let $X$ be a smooth projective $n$-fold such that $q(X)=0$ and $L$ a globally generated, big line bundle on $X$ such that $h^0(K_X+(n-2)L) >0$. We give necessary and sufficient conditions for the adjoint systems $|K_X+kL|$ to be birational for $k \geq n-1$. In particular, for Calabi-Yau $n$-folds we generalize and prove parts of a conjecture of Gallego and Purnaprajna.
We will prove the following results for $3$-fold pairs $(X,B)$ over an algebraically closed field $k$ of characteristic $p>5$: log flips exist for $\Q$-factorial dlt pairs $(X,B)$; log minimal models exist for projective klt pairs $(X,B)$ with pseudo-effective $K_X+B$; the log canonical ring $R(K_X+B)$ is finitely generated for projective klt pairs $(X,B)$ when $K_X+B$ is a big $\Q$-divisor; semi-ampleness holds for a nef and big $\Q$-divisor $D$ if $D-(K_X+B)$ is nef and big and $(X,B)$ is projective klt; $\Q$-factorial dlt models exist for lc pairs $(X,B)$; terminal models exist for klt pair…
Quadratic generation of ideals defining nonsigular toric 3-folds
针对两类非奇异环三维簇上的丰富线丛，证明其射影正规嵌入对应的理想可由二次元素生成。
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.
We construct Calabi-Yau 3-folds as orbifolds embedded in weighted projective space in codimension 4. For each Hilbert series that is realised, there are at least two different components of Calabi-Yau 3-folds.
In this paper, we prove that for a fibration $f:X\to Z$ from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ with $\mathrm{char} k =p >5$, if the geometric generic fiber $X_{\overlineη}$ is smooth, then subadditivity of Kodaira dimensions holds, i.e. $$κ(X)\geκ(X_{\overlineη})+κ(Z).$$
Nonsingular projective 3-folds $V$ of general type can be naturally classified into 18 families according to the {\it pluricanonical section index} $δ(V):=\text{min}\{m|P_m\geq 2\}$ since $1\leq δ(V)\leq 18$ due to our previous series (I, II). Based on our further classification to 3-folds with $δ(V)\geq 13$ and an intensive geometrical investigation to those with $δ(V)\leq 12$, we prove that $\text{Vol}(V) \geq \frac{1}{1680}$ and that the pluricanonical map $Φ_{m}$ is birational for all $m \geq 61$, which greatly improves known results. An optimal birationality of $Φ_m$ for the case $δ(V)=2$…
A formula for the irregularity of abelian coverings of the projective plane is established and some applications are presented.
We prove that the universal cover of a normal, projective variety X is quasi-projective if and only if a finite, étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.
We classify minimal projective 3-folds of general type with $p_g = 2$ by studying the birationality of their 6-canonical maps.
The 5-canonical system on 3-folds of general type
设$X$是具有典型奇点的一般型射影极小Gorenstein 3-折叠.证明了5-正则映射在其象上是双有理的。
Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that $H^j(X,Ω^i_X\otimes L)=0$ for every $j>0$, $i\geq 0$, and $L$ ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano 3-folds that satisfy Bott vanishing. There are many more than expected. Along the way, we conjecture that for every projective birational morphism $π\colon X\to Y$ of smooth varieties, and every line bundle $A$ on $X$ that is ample over $Y$, the higher direct image sheaf $R^jπ_*(Ω^i_X\otimes A)$ is zero for every $j>0$ and $i\geq 0$.
Homological projective duality for Grassmannians of lines
我们证明了Grassmannian簇Gr（2，6）和Gr（2，7）的同调投射对偶簇是由相应Pfavian簇的奇点的某些非交换分解给出的。作为一个应用，我们描述了这些格拉斯曼和普法尔茨的线性部分的导出范畴。特别地，我们证明了：（1）Pfiran三次4-重簇的导出范畴和K3-曲面的导出范畴都有一个由3个例外线丛组成的半正交分解;（2）Gr（2，7）的相互正交的Calabi-Yau线性截面和相应Pfiran簇的相互正交的Calabi-Yau线性截面是等价的.我们还根据三次4重的导出范畴推测了其合理性准则。
Theta constants associated to cubic three folds
对于三次曲面X，Allcock，Carlson和Toledo通过考虑沿X分支的三维射影空间的三重覆盖Y的中间Jacobian J（Y），构造了一个从标记三次曲面族到嵌入Siegel上半空间的5次四维复球的周期映射.本文通过构造J（Y）与射影线在七点分支的循环6重覆盖的Prym簇之间的同构，给出了per的逆的θ常数表达式。
Let $X$ be a nonsingular projective $n$-fold $(n\ge 2)$ of Fano or of general type with ample canonical bundle $K_X$ over an algebraic closed field $κ$ of any characteristic. We produce a new method to give a bunch of inequalities in terms of all the Chern classes $c_1, c_2, \cdots, c_n$ by pulling back Schubert classes in the Chow group of Grassmannian under the Gauss map. Moreover, we show that if the characteristic of $κ$ is $0$, then the Chern ratios $(\frac{c_{2,1^{n-2}}}{c_{1^n}}, \frac{c_{2,2,1^{n-4}}}{c_{1^n}}, \cdots, \frac{c_{n}}{c_{1^n}})$ are contained in a convex polyhedron for al…
We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of a cyclic covering of degree $p$ of the projective line by a Mumford curve over a complete discrete valuation field of positive characteristic $p$. Previously, Bradley studied that of any degree over a non-archimedean local field of characteristic zero.
Let $X$ be a Gorenstein minimal projective $n$-fold with at worst locally factorial terminal singularities, and suppose that the canonical map of $X$ is generically finite onto its image. When $n<4$, the canonical degree is universally bounded. While the possibility of obtaining a universal bound on the canonical degree of $X$ for $n \geqslant 4$ may be inaccessible, we give a uniform upper bound for the degrees of certain abelian covers. In particular, we show that if the canonical divisor $K_X$ defines an abelian cover over $\mathbb{P}^n$, i.e., when $X$ is an \emph{abelian canonical $n$-fol…
On cyclic covers of the projective line
本文构造了射影线的循环复盖的构形空间，并给出了曲线在给定自同构群下的轨迹。作为一个应用程序，我们提供的例子，任意高属定义在其领域的模，而不是超椭圆。
In this note we present two equivalent definitions for the genus of a birational map X --> Y between smooth complex projective 3-folds. The first one is the definition introduced in 1973 by M. A. Frumkin, the second one was recently suggested to me by S. Cantat. By focusing first on proving that these two definitions are equivalent, one can obtain all the results of the paper of Frumkin in a much shorter way. In particular, the genus of an automorphism of $\mathbb{C}^3$, view as a birational self-map of the projective space, will easily be proved to be 0.
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
We give a lower bound on the rank of the Cartier operator of Jacobian varieties of hyperelliptic and superelliptic curves in terms of their genus.
We construct a deformation family for each of the 34 Hilbert series of index 2 Fano 3-folds. In 18 cases we construct two different families, distinguished by the topology of their general members.
We study compact Kähler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from $L^2$ -theory, Campana's geometric orbifolds and the minimal model program we show that this condition imposes strong restrictions on the geometry of X. In particular we prove that if a projective threefold with infinite fundamental group has a quasi-projective universal cover, the latter is then isomorphic to the product of an affine space with a simply connected manifold.
We consider families of cyclic covers of the projective line, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are precisely twenty such families that give rise to a special subvariety in the moduli space of abelian varieties. Our proof uses techniques in mixed characteristics due to Dwork and Ogus.
Cyclic coverings of the $p$-adic projective line by Mumford curves
本文用两种方法计算了$p$ -adic射影直线被Mumford曲线循环覆盖的分支点位置的精确界。首先利用Fumiharu Kato的 *-树，然后利用组合群论给出了射影直线上Mumford曲线所对应的Schottky群的显式矩阵表示.
Theta constants associated with the cyclic triple coverings of the complex projective line branching at six points
设$ψ$是复射影线分支于六点的循环三重覆盖族的周期映射。对称群$S_6$作用于这个族及其在$ψ.$下的象本文给出了$ψ^{-1}$关于15个θ常数的$S_6$ -等变表达式.
Ulrich bundles on double covers of projective spaces
本文证明了任意射影空间二重覆盖的光滑射影簇都容许Ulrich丛，并在二维情形下构造了秩为二的Ulrich丛。
We investigate the resurgence and asymptotic resurgence numbers of fiber products of projective schemes. Particularly, we show that while the asymptotic resurgence number of the k-fold fiber product of a projective scheme remains unchanged, its resurgence number could strictly increase.
Studying coverings over algebraic varieties is an effective method in algebraic geometry. By combining the technique of triple cover from Miranda and Tan, we proved that if the degree of the branch divisor of a normal triple cover over $¶^2$ is no more than $18$ and not equal to $16$, then the trace-free bundle of the triple cover is uniform. Moreover, we totally classified all these trace-free bundles.
We show that if an ample line bundle L on a nonsingular toric 3-fold satisfies h^0(L+2K)=0, then L is normally generated. As an application, we show that the anti-canonical divisor on a nonsingular toric Fano 4-fold is normally generated.
In this paper we prove birational superrigidity of finite covers of degree $d$ of the $M$-dimensional projective space of index 1, where $d\geqslant 5$ and $M\geqslant 10$, with at most quadratic singularities of rank $\geqslant 7$, satisfying certain regularity conditions. Up to now, only cyclic covers were studied in this respect. The set of varieties with worse singularities or not satisfying the regularity conditions is of codimension $\geqslant\frac12(M-4)(M-5)+1$ in the natural parameter space of the family.
Let X be a smooth complex projective variety of dimension 4 and let L be an ample line bundle on X. In this paper, we study a natural number m such that h^{0}(m(K_{X}+L))>0 for any polarized 4-folds (X,L) with κ(K_{X}+L)\geq 0.
We prove the following results for projective klt pairs of dimension $3$ over an algebraically closed field of char $p>5$: the cone theorem, the base point free theorem, the contraction theorem, finiteness of minimal models, termination with scaling, existence of Mori fibre spaces, etc.
Notes on very ample vector bundles on 3-folds
设$\Cal E$是光滑复三重射影$X$上秩为2的非常充分的向量丛.当$K_X+\det \Cal E$是nef但不是big时，当$K_X+\det \Cal E$的适当的正倍数定义了一个态射$X\to B$，其纤维连通到光滑的射影曲线$B$上，其中$K_X$是$X$的标准丛时，给出了关于$\Cal E$的第三Segre类的一个不等式.作为应用，研究了$B$的亏格为正且$\Cal E$具有全局截面且零轨迹为亏格$\geq 2$的光滑超椭圆曲线的情形，将我们以前的结果改进了三倍.
Images of toric variety and amplified endomorphism of weak Fano threefolds
证明Picard秩为2的弱Fano三维流形若为射影环面簇的像则是环面的，并证明具有放大自同态的此类流形也是环面的。
Toroidalization of birational morphisms of 3-folds
我们证明了在特征为零的域上，通过对域和目标上的点和非奇异曲线进行一系列的爆破，可以使射影3-折叠的双有理态射成为环面。
Bound of automorphisms of projective varieties of general type
证明了存在一个仅依赖于$n$的正数$C_{n}$，使得对于{ \bf C}上定义的一般型$X$的光滑射影$n$ -fold，自同构群$Aut(X)$满足不等式$\sharp{Aut}(X)\leq C_{n}\cdotμ(X,K_{X})$，其中$μ(X,K_{X})$是$X$关于$K_{X}$的体积.
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。