Coble surfaces with finite automorphism group

Coble曲面和节点Enriques曲面的模空间的合理性

The rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces

证明了复数域上Coble曲面和节点Enriques曲面的粗模空间的合理性。

Coble's question and complex dynamics of inertia groups on surfaces

We study the inertia groups of some smooth rational curves on 2-elementary K3 surfaces and singular K3 surfaces from the view of topological entropy, with an application to a long standing open question of Coble on the inertia group of a generic Coble surface.

Biregular and birational geometry of quartic double solids with 15 nodes

Three-dimensional del Pezzo varieties of degree 2 are double covers of projective space $\mathbb{P}^{3}$ branced in a quadric. In this paper we prove that if a del Pezzo variety of degree 2 has exactly 15 nodes then the corresponding quadric is a hyperplane section of the Igusa quartic or, equivalently, all such del Pezzo varieties are members of one particular linear system on the Coble fourfold. Their automorphism groups are induced from the automorphism group of Coble fourfold. Also we classify all $G$-birationally rigid varieties of such type.

来自 $\mathbb Q$-Gorenstein 形变的 Coble-Mukai 格

The Coble-Mukai lattice from $\mathbb Q$-Gorenstein deformations

本研究通过Coble曲面的Q-Gorenstein光滑化探究Enriques曲面的几何性质，明确将一般纤维的Enriques格与Coble-Mukai格等同，并给出其在平凡典范类Gorenstein Q-同调射影平面上的应用。

The geometry of the Coble cubic and orbital degeneracy loci

The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of alternating trivectors in nine variables. Exploring this relation further, we show how the Hilbert scheme of pairs of points on an abelian surface, and also its Kummer fourfold, a very remarkable hyper-Kähler manifold, can very naturally be constructed in this context. Moreover, we explain how this perspective allows us to describe the group law of an abelian surface, in a strik…

Automorphisms of unnodal Enriques surfaces

It follows from an observation of A. Coble in 1919 that the automorphism group of an unnodal Enriques surface contains the $2$-congruence subgroup of the Weyl group of the $E_{10}$-lattice. In this article, we determine how much bigger the automorphism group of an unnodal Enriques surface can be. Furthermore, we show that the automorphism group is in fact equal to the $2$-congruence subgroup for generic Enriques surfaces in arbitrary characteristic (under the additional assumption that the Enriques surface is ordinary if the characteristic is $2$), improving the corresponding result of W. Bart…

Jacobian Kummer 四重簇的 Coble 对偶性

Coble duality for Jacobian Kummer fourfolds

本文通过 O'Grady 的 theta 群和 Coble 三次簇，建立了 Jacobian 阿贝尔曲面广义 Kummer 四重簇两个奇异模型间的对偶性，并给出任意维奇异 Jacobian Kummer 簇的射影模型，同时构造了 Hilbert 平方上的非自然对合。

Congruence subgroups and Enriques surface automorphisms

We give conceptual proofs of some results on the automorphism group of an Enriques surface X, for which only computational proofs have been available. Namely, there is an obvious upper bound on the image of Aut(X) in the isometry group of X's numerical lattice, and we establish a lower bound for the image that is quite close to this upper bound. These results apply over any algebraically closed field, provided that X lacks nodal curves, or that all its nodal curves are (numerically) congruent to each other mod 2. In this generality these results were originally proven by Looijenga and Cossec-D…

具有大量自同构群的有理曲面

Rational surfaces with a large group of automorphisms

我们分类的有理曲面的自同构群的图像的组的线性变换的Picard组是最大的可能。这回答了Arthur Coble在1928年提出的一个问题，并且可以用无限Coxeter群在射影平面模射影等价的有序点集上的双有理作用的周期轨道来重新表述。我们还概述了大的自同构群的非理性曲面的分类。

通过锥猜想建立自同构群的几何有限性

Geometrical finiteness for automorphism groups via cone conjecture

本文通过锥猜想研究K3、恩里ques、Coble表面及不可约辛流形的自同构群在超球面上的等距作用的几何有限性，证明此类群非正曲率特性，并揭示K3表面的Kleinian晶格与(-2)曲线关系。

模空间与三次曲面的Galois逆问题

Moduli spaces and the inverse Galois problem for cubic surfaces

研究了标记三次曲面的模空间$\widetilde{\calM}$。通过A.\，B. Coble，这有一个紧化$\widetilde{M}$，它被群$W(E_6)$线性作用。$\widetilde{M}$是$\bP^9$中30个立方的交集。对于遗忘标记的态射$\widetilde{calM} \to \bP(1,2,3,4,5)$，紧跟着Clebsch不变映射，我们给出了显式公式.即，Clebsch的不变量是用Coble的无理不变量表示的。作为应用，我们对$\bbQ$上的三次曲面的Galois反问题给出了肯定的回答.

通过根系的Del Pezzo模量

Del Pezzo moduli via root systems

科布尔在1929年的论文中定义了三次曲面和四次曲线的不变量。我们重新解释这些方面的根系的E_6和E_7型，自然与这些品种，从而给他的一些结果一个更内在的治疗。我们的讨论是统一的所有Del Pezzo曲面的次数为2，3，4，5。

Automorphism groups of compact complex surfaces

We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational to a product of an elliptic and a rational curve.

Fano type surfaces with large cyclic automorphisms

We give a characterization of Fano type surfaces with large cyclic automorphisms.

数值Godeaux曲面上的三阶自同构

Automorphisms of order three on numerical Godeaux surfaces

我们证明了数值Godeaux曲面不能有三阶自同构。

Del Pezzo surfaces with infinite automorphism groups

We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.

Gizatullin曲面自同构群的传递性

Transitivity of automorphism groups of Gizatullin surfaces

我们证明了光滑Gizatullin曲面的某个子类的自同构群是由A1-纤维化的自同构生成的，该曲面具有一个特殊的刚性扩张因子。此外，这样的表面提供了光滑的Gizatullin表面的例子与自同构群的非传递作用。因此，它们是Gizatullin猜想的反例。对于这类曲面，在某些特殊情况下，我们给出了自同构群的自然作用的显式轨道。此外，我们提出了他们的自同构群作为两个子群的合并产品。

Du Val del Pezzo曲面的自同构群

Automorphisms of Du Val del Pezzo surfaces

该研究针对自同构群为无限群的Du Val del Pezzo曲面，给出了其自同构群的描述结果。

Automorphism groups of certain Enriques surfaces

We calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general $n$-nodal Enriques surfaces and very general cuspidal Enriques surfaces. We also describe the action of the automorphism group on the set of smooth rational curves and on the set of elliptic fibrations.

Order 9 automorphisms of K3 surfaces

In this paper we provide a complete classification of non-symplectic automorphisms of order nine of complex K3 surfaces.

A surface birational to an Enriques surface with non-finitely generated automorphism group

We will show that there is a smooth complex projective surface, birational to some Enriques surface, such that the automorphism group is discrete but not finitely generated.

A1-fibered曲面的自同构

Automorphisms of A1-fibered surfaces

我们发展了双有理几何的技巧来研究具有许多不同有理纤维化的仿射曲面的自同构，特别关注自同构与这些纤维化之间的相互作用。特别是，我们关联到每个表面$S$的这种类型的一个图形编码等价类的合理纤维化，从它可以决定，例如，如果自同构群的$S$是由自同构保持这些纤维化。

On the characterization of Danielewski surfaces by their automorphism group

In this note we show that if the automorphism group of a normal affine surface $S$ is isomorphic to the automorphism group of a Danielewski surface, then $S$ is isomorphic to a Danielewski surface.

一类奇异K3曲面和Enriques曲面的自同构群

The automorphism groups of certain singular K3 surfaces and an Enriques surface

本文给出了三个奇异K3曲面的全自同构群的生成元的有限集合，其中六次交错群在这三个曲面上辛作用。我们还提出了一个有限的一组发电机的全自同构群的相关联的Enriques表面，在其上的Mathieu组M_{10}的行为。

具有大阿贝尔群的自同构的Riemann surfaces

Riemann surfaces with a large abelian group of automorphisms

本文对具有大的自同构阿贝尔群的黎曼曲面进行了分类，即具有严格大于$4(g-1)$阶的自同构阿贝尔群的黎曼曲面，其中$g$通常表示黎曼曲面的亏格。

K3 surface entropy and automorphism groups

We derive a characterization of the complex projective K3 surfaces which have automorphisms of positive entropy in term of their Néron-Severi lattices. Along the way, we classify the projective K3 surfaces of zero entropy with infinite automorphism groups and we determine the projective K3 surfaces of Picard number at least five with almost abelian automorphism groups, which gives an answer to a long standing question of Nikulin.

具有11阶自同构的K3曲面

K3 surfaces with an automorphism of order 11

本文研究了具有任意特征的11阶自同构的K3曲面。具体来说，我们研究野生的情况下，并证明，一般这样的表面的特征11皮卡数为2。我们还构造了K3曲面，在每个特征中具有11阶自同构，并尽可能地构造超奇异K3曲面。

曲面上点空间的自然自同构

Automorphismes naturels de l'espace de Douady de points sur une surface

本文证明了关于曲面上点的Douady空间的自同构自同构群的大小的一些一般性结果。然后，我们研究了一些性质的自同构来自一个自同构的表面，特别是他们的行动上同调和分类的不动点。

Automorphism groups of Inoue and Kodaira surfaces

We prove that automorphism groups of Inoue and primary Kodaira surfaces are Jordan.

Minimum positive entropy of complex Enriques surface automorphisms

We determine the minimum positive entropy of complex Enriques surface automorphisms. This together with McMullen's work completes the determination of the minimum positive entropy of complex surface automorphisms in each class of Enriques-Kodaira classification of complex surfaces.

Automorphisms of cubic surfaces without points

We classify finite groups acting by birational transformations of a non-trivial Severi--Brauer surface over a field of characteristc zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism group of a smooth cubic surface over a field $K$ of characteristic zero that has no $K$-points is abelian, and find a sharp bound for the Jordan constants of birational automorphism groups of such cubic surfaces.

Automorphisms of quasi-projective surfaces over fields of finite characteristic

We prove that the group of automorphisms of any quasi-projective surface $S$ in finite characteristic has the $p$-Jordan property.

复K3曲面自同构的循环群

Cyclic groups of automorphisms of complex K3 surfaces

我们确定了复K3曲面的自同构的所有可能的阶。正整数N是复K3曲面的自同构的阶当且仅当$ϕ(N) \leq 20$，其中$ϕ$是欧拉函数。

具有外伽罗瓦点的四次曲面与具有4阶自同构的K3曲面

Quartic surfaces with an outer Galois point and K3 surfaces with an automorphism of order 4

本文建立了具有外伽罗瓦点的光滑四次曲面与具有特定4阶自同构的K3曲面之间的一一对应，并进一步用K3曲面刻画了具有两个及以上外伽罗瓦点的四次曲面。

奇特征下del Pezzo曲面的自同构

Automorphisms of del Pezzo surfaces in odd characteristic

本文在奇正特征的代数闭域上，完成了del Pezzo曲面自同构群的分类工作。

作用于Néron-Severi格的K3曲面上的非辛自同构的分类

Classification of non-symplectic automorphisms on K3 surfaces which act trivially on the Néron-Severi lattice

我们处理$K3$曲面上的非辛自同构，这些曲面对Néron-Severi格起平凡作用。本文对$K3$曲面上的素幂阶，特别是2幂阶的非辛自同构进行了分类，即，我们描述了它们的固定轨迹。

一类K3曲面族的自同构群

Automorphism groups in a family of K3 surfaces

给出了关于“自同构群在K3曲面模的特殊点处变大”的几个事实。证明了在任意一维非平凡射影K3曲面族中，自同构群在稠密子集上是无限阶的。

On Enriques surfaces in characteristic 2 with a finite group of automorphisms

Complex Enriques surfaces with a finite group of automorphisms are classified into seven types. In this paper, we determine which types of such Enriques surfaces exist in characteristic 2. In particular we give a one dimensional family of classical and supersingular Enriques surfaces with the automorphism group isomorphic to the symmetric group of degree five.

On automorphisms and the cone conjecture for Enriques surfaces in odd characteristic

We prove that, for an Enriques surface in odd characteristic, the automorphism group is finitely generated and it acts on the effective nef cone with a rational polyhedral fundamental domain. We also construct a smooth projective surface in odd characteristic which is birational to an Enriques surface and whose automorphism group is discrete but not finitely generated.

Automorphism groups of rational elliptic and quasi-elliptic surfaces in all characteristics

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such surfaces that admit non-trivial automorphisms that act trivially on the Picard group. As an application, we classify classical Enriques surfaces in characteristic $2$ that admit non-trivial numerically trivial automorphisms.

一类K3曲面的自同构群

On automorphisms group of some K3 surfaces

本文研究光滑六次平面曲线上分歧的射影平面的双覆盖K3曲面的自同构群。更确切地说，我们研究了皮卡德秩2的K3曲面的一些特殊情况。

Classification of Enriques surfaces with finite automorphism group in characteristic 2

We classify supersingular and classical Enriques surfaces with finite automorphism group in characteristic 2 into 8 types according to their dual graphs of all $(-2)$-curves (nonsigular rational curves). We give examples of these Enriques surfaces together with their canonical coverings. It follows that the classification of all Enriques surfaces with finite automorphism group in any characteristics has been finished.

Some examples of K3 surfaces with infinite automorphism group which preserves an elliptic pencil

We give more details to our examples in [9] of K3 surfaces over C such that they have infinite automorphism group but it preserves some elliptic pencil of the K3

任意特征Enriques曲面的数值平凡自同构

Numerical trivial automorphisms of Enriques surfaces in arbitrary characteristic

我们推广到任意特征的一些已知结果的自同构复杂的Enriques曲面，平凡的上同调或上同调模挠。

Surface fibrations with large equivariant automorphism group

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of fibre genus $g\ge 1$ with smooth generic fibre over an arbitrary algebraically closed field $\mathbf{k}$ whose equivariant automorphism group is infinite.

具有单自同构群的Log del Pezzo曲面

Log del Pezzo surfaces with simple automorphism groups

本文研究了有限单群作用的仅具对数终端奇点的del Pezzo曲面。

关于K3曲面的辛与非辛自同构

On symplectic and non--symplectic automorphisms of K3 surfaces

本文研究了一类K3曲面族中允许有穷级的非辛自同构的通有成员何时也允许同阶的辛自同构。如果自同构的阶是素数，我们给出了这个问题的一个完整的答案，否则，我们提供了几个例子和部分结果。证明了在一定条件下，一个含有素奇阶非辛自同构$p$的K3曲面也含有$2p$阶非辛自同构.这推广了J.Dillies以前对$p=3$的一个结果。

超奇异K3曲面上的动力学和Salem度为22的自同构

Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22

本文系统地给出了所有p同余3 mod 4的素数在Artin不变1的超奇异K3曲面上的最大Salem度为22的显式自同构。Salem度为22的自同构不提升到任何特征零模型。

有理三维簇与Kummer曲面的伪自同构

Pseudo-automorphisms of rational threefolds and Kummer surfaces

本文将45个经典Kummer曲面自同构提升为$\mathbb{P}^3$沿6点15线爆破所得三维簇的伪自同构，并描述了由这些已知伪自同构生成的群的基本域。

一般射影K3曲面上两点的Hilbert方案的自同构群

The automorphism group of the Hilbert scheme of two points on a generic projective K3 surface

我们确定的希尔伯特计划的两个点上的一般射影K3曲面的任何极化的自同构群。我们获得特别是新的例子希尔伯特计划的点具有非自然的非辛自同构。这些自同构的存在依赖于Pell方程的解。

Automorphisms of K3 surfaces and their applications

This paper is a survey about $K3$ surfaces with an automorphism and log rational surfaces, in particular, log del Pezzo surfaces and log Enriques surfaces. It is also a reproduction on my talk at "Mathematical structures of integrable systems and their applications" held at Research Institute for Mathematical Sciences in September 2018.

Automorphisms of cubic surfaces in positive characteristic

We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that the moduli space of smooth cubic surfaces is rational in every characteristic, determine the dimensions of the strata admitting each possible isomorphism class of automorphism group, and find explicit normal forms in each case. Finally, we completely characterize when a smooth cubic surface in positive characteristic, together with a group action, can be lift…

Projective Automorphism Groups of Nonsingular Quartic Surfaces

For every p >= 5, we determine all Z_p-invariant nonsingular quartic surfaces in the three dimensional projective space over an algebraically closed field of characteristic zero. In some cases, we also determine their full projective automorphism groups.

具有非辛自同构的K3曲面和具有循环群的积商曲面

K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups

本文对两条曲线乘积之商$C_1\times C_2$的极小模型K3曲面，通过$\Z/p\Z$群或$\Z/2p\Z$群的对角作用进行分类.这些K3曲面允许由曲线$C_1$或$C_2$之一的自同构引起的$p$阶的非辛自同构。我们证明了大多数允许$p$阶非辛自同构的K3曲面（实际上是具有$p$阶非辛自同构的K3曲面的模空间的极大不可约分支）都是这样得到的.另外，我们证明了在更严格的假设下，可以得到相同的K3曲面集，即两条曲线中的一条，比如说$C_2$，同构于一条具有阶为$p$的自同构$δ_p$的刚性超椭圆曲线，并且K3曲面的自同构是由$δ_p$诱导的.最后，我们描述了所构造的曲面的霍奇结构的变化，并给出了其中一些曲面的方程。