发帖
雷达卡
摘要翻译：
本文的第一个主要目的是改进已有的关于P_g(S)=0$的一般型复射影曲面及其模空间的知识，构造了19个新的具有未知基群的复射影曲面族。我们还提供了一个包含所有k^2<=7的已知曲面的表。我们的第二个主要目的是更一般化地描述光滑射影变体的基本群，它们在有限群的作用下表现为曲线乘积的商的极小分解。在二维情况下，我们把所有Q=P_g=0作为这样一个商的最小分辨率而得到的具有有理双点的曲面归类为奇点。我们证明了所有这些曲面都为Bloch猜想提供了证据。
---
英文标题：
《Quotients of products of curves, new surfaces with $p_g=0$ and their
fundamental groups》
---
作者：
Ingrid Bauer, Fabrizio Catanese (Universitaet Bayreuth), Fritz
Grunewald (Universitaet Duesseldorf), Roberto Pignatelli (Universita' di
Trento)
---
最新提交年份：
2009
---
分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
一级分类：Mathematics 数学
二级分类：Group Theory 群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
--
---
英文摘要：
The first main purpose of this paper is to contribute to the existing knowledge about the complex projective surfaces $S$ of general type with $p_g(S) = 0$ and their moduli spaces, constructing 19 new families of such surfaces with hitherto unknown fundamental groups. We also provide a table containing all the known such surfaces with K^2 <=7. Our second main purpose is to describe in greater generality the fundamental groups of smooth projective varieties which occur as the minimal resolutions of the quotient of a product of curves by the action of a finite group. We classify, in the two dimensional case, all the surfaces with q=p_g = 0 obtained as the minimal resolution of such a quotient, having rational double points as singularities. We show that all these surfaces give evidence to the Bloch conjecture.
---
PDF链接：
https://arxiv.org/pdf/0809.3420
京公网安备 11010802022788号
