Del Pezzo surfaces of degree 2 and jacobians without complex multiplication

Weighted complete intersection del Pezzo surfaces

We classify codimension 2 well-formed and quasi-smooth weighted complete intersection del Pezzo surfaces.

DelPezzo纤维化的双有理映射

Birational maps of del Pezzo fibrations

本文研究了平滑曲线芽上非奇异delPezzo纤维化的刚性。

关于具有du Val奇点的del Pezzo表面的核心正则性

On the coregularity of del Pezzo surfaces with du Val singularities

研究了具有du Val奇点的del Pezzo表面的核心正则性，发现正核心正则性表面对应于具有特殊性质的非平凡椭圆纤维化，且大多数表面核心正则性为0。

Unstable singular del Pezzo hypersurfaces with lower index

We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.

log del Pezzo曲面上的最大奇点个数

The maximal number of singular points on log del Pezzo surfaces

证明了Picard数为1的del Pezzo曲面至多有4个奇点.

关于1次DelPezzo纤维化的一点注记

A note on del Pezzo fibrations of degree 1

我们研究了具有终端奇点的1度delPezzo纤维化。本文将研究一次del Pezzo曲面上的奇异性与Kodaira椭圆奇异纤维分类之间的联系。通过这一研究，我们得到了关于具有终端奇点的一次delPezzo纤维化的双有理映射的几个结果。

Interpolation Problems: Del Pezzo Surfaces

We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.

关于4次Del Pezzo曲面的模

On the moduli of degree 4 Del Pezzo surfaces

研究了曲线上四次Del Pezzo曲面纤维化族的不可约性。

一次和二次Del Pezzo曲面上的有理点

Rational Points on Del Pezzo Surface of degree 1 and 2

讨论了有限域$\mathbb F_q$上1次和2次del Pezzo曲面上的有理点，给出了具有唯一有理点的del Pezzo曲面的显式方程.

K-stability of log del Pezzo hypersurfaces with index 2

We completely classify K-stability of log del Pezzo hypersurfaces with index 2.

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。

Del Pezzo曲面的退化与二次曲线Hilbert格式的Gromov-Witten不变量

Degenerations of Del Pezzo surfaces and the Gromov-Witten invariants of the Hilbert Scheme of conics

利用退化方法研究了Del Pezzo曲面的示性数。

Cylinders in del Pezzo surfaces with du Val singularities

We consider del Pezzo surfaces with du Val singularities. We'll prove that a del Pezzo surface $X$ with du Val singularities has a $-K_X$-polar cylinder if and only if there exist tiger such that the support of this tiger does not contain anti-canonical divisor. Also we classify all del Pezzo surfaces $X$ such that $X$ has not any cylinders.

Delta invariants of singular del Pezzo surfaces

We estimate $δ$-invariants of some singular del Pezzo surfaces with quotient singularities, which we studied ten years ago. As a result, we show that each of these surfaces admits an orbifold Kähler--Einstein metric.

具有四个log终端奇点的Del Pezzo表面

Del Pezzo surfaces with four log terminal singularities

本文研究了Picard数为一且具有四个log终端奇点的Del Pezzo表面的分类问题。

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.

大体积的Log del Pezzo表面

Log del Pezzo surfaces with large volumes

我们对所有指数为$a$的log del Pezzo曲面$S$进行分类，使得体积$(-K_S^2)$大于或等于$2a$。

RDP del Pezzo surfaces with global vector fields in odd characteristic

We classify RDP del Pezzo surfaces with global vector fields over arbitrary algebraically closed fields of characteristic $p \neq 2$. In characteristic $0$, every RDP del Pezzo surface $X$ is equivariant, that is, ${\rm Aut}_X = {\rm Aut}_{\widetilde{X}}$, where $\widetilde{X}$ is the minimal resolution of $X$, hence the classification of RDP del Pezzo surfaces with global vector fields is equivalent to the classification of weak del Pezzo surfaces with global vector fields. In this article, we show that if $p \neq 2,3,5,7$, then it is still true that every RDP del Pezzo surface is equivariant…

Equivariant birational geometry of quintic del Pezzo surface

In this paper we prove that there are exactly two $G$-minimal surfaces which are $G$-birational to the quintic del Pezzo surface, where $G \cong C_5 \rtimes C_4$. These surfaces are the quintic del Pezzo surface itself and the surface $\mathbb{P}^1 \times \mathbb{P}^1$.

Klt del Pezzo surfaces which are not globally F-split

We construct a klt del Pezzo surface which is not globally F-split, over any algebraically closed field of positive characteristic.

del Pezzo曲面上有理曲线空间的不可约性

The irreducibility of the spaces of rational curves on del Pezzo surfaces

我们证明了del Pezzo曲面上的有理曲线的空间要么是不可约的要么是空的，只有一个唯一的例外。

具有唯一奇点的秩2和Cartier指数3的Log del Pezzo曲面

Log del Pezzo Surfaces of Rank 2 and Cartier Index 3 with a Unique Singularity

Log del Pezzo表面起着与一般类型表面相反的作用。我们将完全分类所有的log del Pezzo表面的秩2和Cartier指数3与唯一的奇异性。

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。

Del Pezzo foliations with log canonical singularities

In this paper, we classify del Pezzo foliations on projective manifolds of rank at least 3 and with log canonical singularities in the sense of McQuillan.

$\mathbb{G}_a^3$-structures on del Pezzo fibrations

In this paper we prove that del Pezzo fibrations admit $\mathbb{G}_{a}^{3}$-structures if and only if they are $\mathbb{P}^2$-bundles over $\mathbb{P}^{1}$.

几乎del Pezzo流形

Almost del Pezzo manifolds

我们分类几乎del Pezzo流形在任意维n，即，具有大小不等的反正则丛-K_X的射影流形X，使得-K_X可被n-1整除.

Birational rigidity of $G$-del Pezzo threefolds of degree 2

In this paper we classify nodal rational non-$\mathbb{Q}$-factorial del Pezzo threefolds of degree 2 which can be $G$-birationally rigid for some subgroup $G\subset \operatorname{Aut}(X)$.

Potentially stably rational del Pezzo surfaces over nonclosed fields

We classify Galois actions on Picard lattices of del Pezzo surfaces of degrees 1,2, and 3 giving rise to minimal surfaces with no cohomological obstructions to stable rationality.

分数阶不小的Log del Pezzo曲面

Log del Pezzo surfaces with not small fractional indices

对于log del Pezzo曲面$S$，分数索引$r(S)\in\mathbb{Q}_{>0}$是$r$的最大值，利用该最大值，$-K_S$可以被写为$r$乘以某个卡地亚除数。本文在Nakayama的方法的基础上，用$S$对所有的原木del Pezzo表面进行了分类。

Gorenstein正则del Pezzo曲面上的对数正则阈值

Log canonical thresholds on Gorenstein canonical del Pezzo surfaces

我们分类所有有效的反正则因子弱del Pezzo曲面。通过这种分类，我们得到的有效anticanonical因子在给定的Gorenstein典型del Pezzo表面的对数典型阈值之间的最小数目。

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。

低次数 del Pezzo 轨形分类 II

Classification of low degree del Pezzo orbifolds II

本文在 Campana 框架下，对次数小于 6 的 del Pezzo 轨形按边界分量进行分类，补充了先前不可约边界情形的工作。

DelPezzo纤维化的双有理模型

Birational models of del Pezzo fibrations

这是课堂讲稿系列的论文初稿。

具 du Val 奇点的 del Pezzo 曲面的复杂度

Complexity of del Pezzo surfaces with du Val singularities

该研究针对具 du Val 奇点的 del Pezzo 曲面，完成了其复杂度的计算工作。

无反典范极柱面的K-不稳定奇异del Pezzo曲面

K-unstable singular del Pezzo surfaces without anticanonical polar cylinder

该研究证明了存在既不具备K-半稳定性也不含反典范极柱面的奇异del Pezzo曲面，丰富了代数几何中相关曲面的性质研究。

Asymptotic Chow stability of toric Del Pezzo surfaces

In this short note, we study the asymptotic Chow polystability of toric Del Pezzo surfaces appear in the moduli space of Kähler-Einstein Fano varieties constructed in [OSS16].

Birational rigidity of orbifold degree 2 del Pezzo fibrations

Varieties fibered into del Pezzo surfaces form a class of possible outputs of the minimal model program. It is known that del Pezzo fibrations of degrees $1$ and $2$ over the projective line with smooth total space satisfying the so-called $K^2$-condition are birationally rigid: their Mori fibre space structure is unique. This implies that they are not birational to any Fano varieties, conic bundles or other del Pezzo fibrations. In particular, they are irrational. The families of del Pezzo fibrations with smooth total space of degree $2$ are rather special, as for "most" families a general de…

指数为2的log del Pezzo曲面方程

Equations of log del Pezzo surfaces of index 2

C上对数末端奇点指数为\le 2的Del Pezzo曲面由Alekseev和Nikulin分类。在本文中，对于这些曲面中的每一个，我们找到一个适当的态射到射影空间。这些态射使我们能够在某些加权射影空间中用方程描述指数为\le 2的del Pezzo曲面。得到的结果是自然完成的类似结果的杜瓦尔，和Hidaka和渡边，描述德尔佩佐表面的指数为1。

准线性作用于del Pezzo表面的理查德几何

Birational geometry of actions on del Pezzo surfaces

本文完成有限群在del Pezzo表面的正则一般自由作用的分类，解决了若干等变理查德几何中的开放问题。

奇异 del Pezzo 曲面上的刚性仿射锥

Rigid affine cones over singular del Pezzo surfaces

本文完全确定了指数为1的拟光滑 log del Pezzo 曲面中反典范极化柱的存在性。

Log canonical degenerations of del Pezzo surfaces in Q-Gorenstein families

We classify del Pezzo surfaces of Picard number one with log canonical singularities admitting Q-Gorenstein smoothings.

On exceptional collections of line bundles on weak del Pezzo surfaces

We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3$ is an augmentation in the sense of L.Hille and M.Perling, while for some weak del Pezzo surfaces of degree $2$ the above is not true. We classify smooth projective surfaces possessing a cyclic strong exceptional collection of line bundles of maximal length: we prove that they are weak del Pezzo surfaces and find all types of weak del Pezzo surfaces admitting such a collection. We find simple criteria of exceptional…

具有商奇异性的delPezzo纤维化的双有理刚性及其应用

Birational rigidity of del Pezzo fibrations with quotient singularities and its application

本文给出了仅具有商奇点的1次和2次delPezzo纤维化的双有理刚性的一个判别准则。作为应用，我们证明了适当的del Pezzo纤维化的双有理刚性，承认克莱因单群的作用。

指数为3的原木del Pezzo表面的分类

Classification of log del Pezzo surfaces of index three

一个正规射影非Gorenstein对数终止面$S$称为指数为3的log del Pezzo曲面，如果反典范除子$-3K_S$的3次是充分Cartier因子.我们将指数为3的所有log del Pezzo曲面分类。分类技术基于Nakayama的论点。

Classification of del Pezzo surfaces with $\frac{1}{3}(1,1)$- and $\frac{1}{4}(1,1)$-singularities

We classify all the del Pezzo surfaces with $\frac{1}{3}(1,1)$- and $\frac{1}{4}(1,1)$-singularities having no floating $(-1)$-curves into 39 types.

Stable rationality of del Pezzo fibrations of low degree over projective spaces

The main aim of this article is to show that a very general 3-dimensional del Pezzo fibration of degree 1,2,3 is not stably rational except for a del Pezzo fibration of degree 3 belonging to explicitly described 2 families. Higher dimensional generalizations are also discussed and we prove that a very general del Pezzo fibration of degree 1,2,3 defined over the projective space is not stably rational provided that the anticanonical divisor is not ample.

Movable Bend and Break for sections of del Pezzo fibrations

This is a report of the author's talk at Algebra Symposium 2019 held at Tohoku University. We discuss some improvements of Mori's Bend and Break for sections of del Pezzo fibrations over $\mathbb P^1$.

奇异del Pezzo曲面的Brauer群

Brauer groups of singular del Pezzo surfaces

讨论了有理奇点对曲面Brauer群的影响，并计算了代数闭域上所有奇异del Pezzo曲面的Brauer群.

1次和2次del Pezzo曲面束的双有理性质

Birational properties of pencils of del Pezzo surfaces of degree 1 and 2

研究了1次和2次del Pezzo曲面上光滑Mori纤维化的双有理刚性问题。对于1度，我们得到了刚性和非刚性情况的完整描述。

Hilbert functions of Cox rings of del Pezzo surfaces

To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green-Lazarsfeld indices, the projective dimensions, and the Castelnuovo-Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four.

关于Gorenstein log del Pezzo曲面

On Gorenstein log del Pezzo Surfaces

本文首先给出了Picard数1 Gorenstein log del Pezzo曲面的奇异类型的完整列表以及与给定奇异类型同构的类的个数。然后给出了一种求Gorenstein log del Pezzo曲面所有奇异类型的方法。作为一个应用，我们提出了完整的列表的Dynkin型的Picard数2 Gorenstein日志del Pezzo表面。最后给出了相对极小Gorenstein log del Pezzo曲面的奇异类型的完整列表以及与给定奇异类型同构的类的个数。

弱Del Pezzo曲面的奇异性和实结构的算法

Algorithms for singularities and real structures of weak Del Pezzo surfaces

在本文中，我们认为分类的奇点（杜瓦尔）和真正的结构（墙）弱Del Pezzo表面从算法的角度来看。众所周知，弱Del Pezzo曲面的奇异性对应于根子。我们提出了一个算法，计算这些根子系统的分类。我们用唯一的标号来表示根子系统的等价类。这些标签使我们能够构建具有相应奇异配置的弱Del Pezzo曲面的示例。弱Del Pezzo曲面的实结构的等价类也由根子表示。我们提出了一个算法，计算的分类的真实结构。这导致了另一种证明已知的分类为Del Pezzo表面，并将此分类扩展到奇异弱Del Pezzo表面。作为应用，我们对圆线上的实二次曲线族进行了分类。

del Pezzo曲面上的Ulrich三分法

Ulrich Trichotomy on del Pezzo surfaces

该研究通过射影簇上Ulrich丛与箭图表示的对应关系，证明了任意给定极化下部分del Pezzo曲面满足Ulrich三分法，为代数几何中相关曲面的丛理论研究提供了新结论。

Full Degree Two del Pezzo Surfaces over Small Finite Fields

Hirschfeld classified split del Pezzo surfaces of degree at least three whose points are all contained on the lines in the surface. We continue his work and begin the classification of split degree two del Pezzo surfaces over finite fields whose points are all on the fifty-six exceptional curves of the surfaces.