Real forms on rational surfaces

K3曲面上实有理曲线的计数

Counting real rational curves on K3 surfaces

我们提供了一个真正的模拟的Yau-Zaslow公式计数有理曲线的$K3$表面。

K3曲面上的有理曲线

Rational Curves on K3 Surfaces

证明了一般K3曲面上的线性系组存在有理曲线，且超平面类中的所有有理曲线都是小亏格的一般K3曲面上的节点.

Smooth Rational Curves on Singular Rational Surfaces

We classify all complex surfaces with quotient singularities that do not contain any smooth rational curves, under the assumption that the canonical divisor of the surface is not pseudo-effective. As a corollary we show that if $X$ is a log del Pezzo surface such that for every closed point $p\in X$, there is a smooth curve (locally analytically) passing through $p$, then $X$ contains at least one smooth rational curve.

$G$-solid 有理曲面

$G$-solid Rational Surfaces

本文在复数域上分类了 $G$-solid 有理曲面，给出了完整的分类结果。

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.

K3曲面的自有理映射

Self Rational Maps of K3 Surfaces

我们证明了一个非常一般的射影K3曲面不允许有一个至少二次的支配自有理映射。

K3曲面上有理曲线的奇异性

Singularities of Rational Curves on K3 surfaces

证明了一般K3曲面的任一亏格的本原类中的每一条有理曲线都是结点曲线。

Cylinders in rational surfaces

We answer a question of Ciro Ciliberto about cylinders in rational surfaces which are obtained by blowing up the plane at points in general position.

正特征有理曲面上的Kawamata-Viehweg消失

Kawamata-Viehweg Vanishing on Rational Surfaces in Positive Characteristic

利用光滑有理曲面上对数对的W_2（k）提升性质，证明了Kawamata-Viehweg消灭定理在正特征的有理曲面上成立.作为推论，Kawamata-Viehweg消灭定理在正特征的log del Pezzo曲面上成立。

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.

有理ruled surfaces上的秩3稳定丛

Rank-3 stable bundles on rational ruled surfaces

本文比较了有理直纹曲面上秩为3的向量丛关于不同的充分因子稳定的模空间。我们还讨论了这些模空间的不可约性、单合理性和合理性。

K3曲面上的有理曲线和有理点

Rational curves and points on K3 surfaces

研究了K3曲面上代数点的分布。

Smooth rational surfaces violating Kawamata-Viehweg vanishing

We show that over any algebraically closed field of positive characteristic, there exists a smooth rational surface which violates Kawamata-Viehweg vanishing.

函数域上K3曲面有理点的势密度

Potential density of rational points for K3 surfaces over function fields

给出了具有Zerkiki-稠密有理点和N 'eron-Severi秩为1的复函数域上的非等平凡K3曲面的例子.

A categorical invariant for geometrically rational surfaces with a conic bundle structure

We define a categorical birational invariant for minimal geometrically rational surfaces with a conic bundle structure over a perfect field via components of a natural semiorthogonal decomposition. Together with the similar known result on del Pezzo surfaces, this provides a categorical birational invariant for geometrically rational surfaces.

实有理曲面上的曲线逼近

Approximating curves on real rational surfaces

本文给出实有理曲面上简单闭曲线可被光滑有理曲线逼近的拓扑充要条件，并研究了给定复自交数的逼近问题。

关于P^3中一般曲面到一般型曲面的有理映射

On rational maps from a general surface in P^3 to surfaces of general type

研究了P^{3}中一般曲面到一般类型曲面的支配有理映射。我们证明了目标曲面上的限制，以及有理映射的特殊性质。我们表明，一般的表面有一个小的程度没有这样的地图。此外，Catanese的结果略有改善，一般类型的表面的模量的数量，也得到。

The Hilbert schemes of points on surfaces with rational double point singularities

We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst rational double point singularities is irreducible.

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。

Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces

We classify webs of minimal degree rational curves on surfaces and give a criterion for webs being hexagonal. In addition, we classify Neron-Severi lattices of real weak del Pezzo surfaces. These two classifications are related to root subsystems of E8.

Unbounded negativity on rational surfaces in positive characteristic

We give explicit blowups of the projective plane in positive characteristic that contain smooth rational curves of arbitrarily negative self-intersection, showing that the Bounded Negativity Conjecture fails even for rational surfaces in positive characteristic.

曲面上的交错群与有理函数

Alternating groups and rational functions on surfaces

设X是光滑复射影曲面。证明了对任意充分大的m，存在从X到复有理直纹曲面Y的有理支配映射f，使得f是m次泛有限的，且具有交错群Am的单值性.

有理曲面上的有理曲线的线性系

Linear systems of rational curves on rational surfaces

给定特征为零的代数闭域上的射影非奇异有理曲面S上的曲线C，我们关心S上的线性系Lambda的集合Omega_C满足C在Lambda中，dim Lambda > 0，且Lambda的一般成员是一条有理曲线.论文的主要结果给出了Omega_C的完整描述，特别是刻画了Omega_C非空的曲线C。

Rational double points on Enriques surfaces

We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.

Quadric surface bundles over surfaces and stable rationality

We prove a general specialization theorem which implies stable irrationality for a wide class of quadric surface bundles over rational surfaces. As an application, we solve with the exception of two cases, the stable rationality problem for any very general complex projective quadric surface bundle over the projective plane, given by a symmetric matrix of homogeneous polynomials. Both exceptions degenerate over a plane sextic curve and the corresponding double cover is a K3 surface.

一个具有不可数多个实形式的光滑复有理仿射曲面

A smooth complex rational affine surface with uncountably many real forms

本文构造了一个光滑复有理仿射曲面，证明其具有不可数多个互不同构的实形式，揭示了实代数几何中实形式的丰富性与复杂性。

Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds

In this paper, we check that Fano schemes of lines on certain rational cubic fourfolds are birational to Hilbert schemes of two points on K3 surfaces.

Contour curves and isophotes on rational ruled surfaces

The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some fixed vector. Choosing an angle equal to $π/2$ we obtain a special instance of a~isophote -- the so called contour curve. While contours on rational ruled surfaces are rational curves, this is no longer true for the isophotes. Hence we will provide a formula for their genus. Moreover we will show that the only surfaces with a~rational generic contour are just …

关于有理曲面奇点的分类

On the classification of rational surface singularities

给出了有理曲面奇点图分类的一般策略。对于每一个最大的合理二重点配置，我们调查的基本循环中可能的多重性。我们对某些类型的图进行完全分类。这允许将有理奇点的分类扩展到多重性8。我们还讨论了有理分解图的复杂性。

K3曲面上有理曲线的构造

Constructing rational curves on K3 surfaces

我们开发了一个混合特征版本的Mori-Mukai技术，用于在K3曲面上生成有理曲线。我们减少模p，产生有理曲线上产生的K3表面上的有限域，并提升到特征零。作为应用，我们证明了一类二次生成的具有Picard群的复K3曲面都有无穷多条有理曲线.

拓扑曲面的有理实代数模型

Rational real algebraic models of topological surfaces

Comessatti证明了一套真正的点的理性真正的代数表面是一个不可定向曲面，或两个领域，或环面。相反，很容易看出，所有这些曲面都承认一个有理实代数模型。我们证明了，他们承认只有一个合理的真正的代数模型。这是已知的早期只有两个球，环面，射影平面和克莱因瓶。

2-初等K3曲面II模空间的有理性

Rationality of the moduli spaces of 2-elementary K3 surfaces II

证明了具有非辛对合的K3曲面的模空间对于四种变形类型都是有理的。利用已有的结果，证明了除两种经典情形外，其他模空间的合理性.

有理曲面奇点的余切上同调

Cotangent cohomology of rational surface singularities

我们证明了对于所有有理曲面奇点Y，n阶余切上同调群（n >=2）的生成元个数是相同的.对于一大类有理曲面奇点，包括商奇点，这个数也是维数。对于它们，我们得到了相应的Poincare级数的一个显式公式。

超奇异K3曲面上的有理二重点

Rational double points on supersingular K3 surfaces

研究了超奇异$K3$曲面上总Milnor数为21的有理二重点的构型.给出了可能配置的完整列表。作为应用，我们还给出了超奇异$K3$曲面上极值（准）椭圆纤维化的完整列表。

有理曲面上向量丛模的一个注记

A note of moduli of vector bundles on rational surfaces

利用泛扩张讨论了有理曲面上层模的一些关系。这是Maruyama构造向量丛模的Uhlenbeck紧化方法的推广。

Hirzebruch曲面上的四尖有理尖点曲线

Rational cuspidal curves with four cusps on Hirzebruch surfaces

这篇文章的目的是阐明的问题有多少和什么样的尖点的有理尖点曲线上的Hirzebruch表面可以有。我们使用双有理变换来构造有理尖点曲线与四个尖点的Hirzebruch曲面，并找到这些曲线的相关结果。

指数1 Fano超曲面中的有理曲面

Rational surfaces in index-one Fano hypersurfaces

我们给出的第一个证据的猜想，一般的，指数为1，Fano超曲面是不是单理性的：（i）一般点的超曲面是包含在没有合理的表面规则，粗略地说，由低程度的有理曲线，和（ii）一般点是包含在没有图像的Del Pezzo表面。

实有理曲面

Real rational surfaces

本文综述实有理曲面的拓扑与双有理几何研究成果，涵盖其分类与结构性质。

Rational points on K3 surfaces and derived equivalence

We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.

Cox rings of rational surfaces and redundant blow-ups

We prove that the redundant blow-up preserves the finite generation of the Cox ring of a rational surface under a suitable assumption, and we study the birational structure of Mori dream rational surfaces via redundant blow-ups. It turns out that the redundant blow-up completely characterizes birational morphisms of Mori dream rational surfaces with anticanonical Iitaka dimension $0$. As an application, we construct new Mori dream rational surfaces with anticanonical Iitaka dimension $0$ and $-\infty$ of arbitrarily large Picard number.

光滑有理曲面的DG箭图

DG quivers of smooth rational surfaces

设X是光滑有理曲面。我们计算了X上的线丛的完全例外集的DG维数，它是由X的极小模型上的强例外集的扩充而得到的。特别地，我们计算了光滑复曲面的正则DG代数。

Smooth complex projective rational surfaces with infinitely many real forms

We construct a smooth complex projective rational surface with infinitely many mutually non-isomorphic real forms. This gives the first definite answer to a long standing open question if a smooth complex projective rational surface has only finitely many non-isomorphic real forms or not.

Redundant blow-ups of rational surfaces with big anticanonical divisor

We completely classify redundant blow-ups appearing in the theory of rational surfaces with big anticanonical divisor due to Sakai. In particular, we construct a rational surface with big anticanonical divisor which is not a minimal resolution of a del Pezzo surface with only rational singularities, which gives a negative answer to a question raised in a paper by Testa, Várilly-Alvarado, and Velasco.

关于射影四维空间中有理曲面的注记

A note on rational surfaces in projective four-space

证明了在射影四维空间中，以三次或四次为界的光滑有理曲面的次数不超过12。本文还证明了在射影四维空间中，由具有“简单基点“（见正文）的线性系象Fn的光滑有理曲面的次数至多为12。

K3曲面上有理曲线的稠密性

Density of Rational Curves on K3 Surfaces

证明了在强拓扑下，有理曲线的并在非常一般的K3曲面上是稠密的，而椭圆曲线的并在非常一般的K3曲面的第一喷射空间上是稠密的.

Cubic fourfolds, K3 surfaces, and rationality questions

This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and their geometric interpretations, and connections with rationality and unirationality constructions.

实有理曲面是拟单的

Real Rational Surfaces Are Quasi-Simple

我们证明了一个真正的理性（在$\C$）表面是准简单的，即，这样的曲面在变形时由其实结构的拓扑型在实曲面类中确定。

几乎约化基本圈有理曲面奇点的余切上同调

On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

通过计算余切空间$T^{1}$和$T^{2}$的一般维数公式中的修正项，证明了一类有理曲面奇点的余切空间的维数公式.我们得到了有理曲面奇点$X$的对偶图不包含特定类型的构形时，修正项为零，这推广了Theo de Jong关于有理行列式曲面奇点的修正项$c(X)$为零的一个结果.特别地，我们的结果意味着$c(X)$是零的Riemenschneiders拟行列式有理曲面奇性，这也推广了结果的qoutient奇性。

Equivariant derived equivalence and rational points on K3 surfaces

We study arithmetic properties of derived equivalent K3 surfaces over the field of Laurent power series, using the equivariant geometry of K3 surfaces with cyclic groups actions.

Motivic measures of moduli spaces of 1-dimensional sheaves on rational surfaces

We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by computing their motivic measures.

有理曲面上的极值超椭圆纤维化

Extremal hyperelliptic fibrations on rational surfaces

我们考虑具有相对最小纤维化的有理曲面。这样一个曲面的皮卡数是有界的一般纤维的亏格。当Picard数为最大时，我们用奇异纤维刻画了一个Mordell-Weil群为平凡的曲面.此外，我们明确地描述了定义方程。

射影四维空间中12次有理曲面的构造（附Kristian Ranestad）

Construction of rational surfaces of degree 12 in projective fourspace (with an appendix by Kristian Ranestad)

本文的目的是给出射影四维空间中两种不同的具有12次和13个截亏格的光滑有理曲面的构造。特别是，我们建立了五个不同的家庭的存在性光滑的理性曲面在射影四维空间与规定的不变量。

特征为3的Artin不变量为1的超奇异K3曲面上的有理曲线

Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3

本文用多种方法证明了特征3中Artin不变量为1的超奇异K3曲面上112条非奇异有理曲线的存在性。利用这些有理曲线，我们得到了K3曲面上的$(16)_{10}$-构型和$(280_{4}, 112_{10})$-构型.此外，我们还利用Leech格的理论研究了Picard格。112条非奇异有理曲线对应于112个Leech根。

A note about rational surfaces as unions of affine planes

We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.