Root system construction of a compactification of the moduli space of rational surfaces

有理曲面模空间紧化的根系构造

基本信息

批准号：
14540023
负责人：
MATSUZAWA Jun-ichi
金额：
$ 0.77万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540023/
关键词：
cubic surface moduli compactification root system Weyl group configuration space 3次曲面族三次曲面族

项目摘要

Matsuzawa and Naruki :The aim of our research is to study the geometry of surfaces and its moduli from the point of view of Lie group, root systems and Weyl group. We constructed the universal family of marked cubic surfaces from the maximal torus of adjoint group of simple Lie group of type E6. Also we gave defining equation of a cubic surface in terms of root systems. Furthermore we constructed a smooth compactification of the universal family of marked cubic surfaces and gave a Weyl group equivariant mapping to Naruki's compactification of the moduli space of marked cubic surfaces. These constructions enable us to study the geometry of cubic surfaces from the point of view of root systems and Weyl groups. The family of cubic surfaces can be regarded as the configuration space of seven points of projective plane or mojuli space of algebrac curve of genus 3. We found interesting relationship among the geometry of cubic surface, that of algebraic curve of genus 2 and the structure of root system and Weyl groups of type E7, E6, D4.Ishii :He generalized the Mckay correspondence for simple singularities to general quotient surface singularities via Hilbert scheme of G-orbits. He studied the case for 3-dimensional quotient singularities when the group is abelian and gave a local coordinates of a crepant resolution of the singularity as the representation moduli of the McKay quiver. He also gave explicit description of the groups of self-equivalences of derived category on the minimal resolutions.

松沙和Naruki：我们研究的目的是从Lie Group，Root Systems和Weyl组的角度研究表面及其模量的几何形状。我们从E6型简单谎言组的伴随组的最大圆环中构建了普遍的明显立方体表面家族。同样，我们从根系中给出了立方表面的定义方程。此外，我们对标记的立方表面的通用家族构建了平滑的压实，并为Naruki对标记立方表面的模量空间的压缩提供了韦伊尔集团的映射。这些结构使我们能够从根系和Weyl群的角度研究立方体表面的几何形状。立方体表面的家族可以被视为3属的五个射击平面或莫胡里的配置空间。我们发现了立方表面的几何形状之间的有趣关系，即属2的代数曲线的几何形状，以及通过e7，d4.ishi of d4.ishi of Surforiation of System of Surforiation of d4.ishi of e6，d4.iship of the General of Mckay的结构。希尔伯特G-Orbits计划。当该小组是阿贝利安（Abelian）时，他研究了三维商奇异性的案例，并给出了当地的坐标，以奇异性的奇异性分辨率为麦凯Quiver的代表模式。他还对最小决议的派生类别的自我等量组进行了明确描述。