权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Principal Simple-Group-Bundle over an Elliptic Surface

椭圆面上的主单群丛

基本信息

批准号：
12640095
负责人：
NARUKI Isao
金额：
$ 2.24万
依托单位：
Ritsumeikan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

Through the activity of the prvious year, it turned out that the study of principal simple-croup-bundle over- an elliptic surface is in the most interesting case of the excepional groups of the E-type, closely related with the study of the q-quantization of a del-Pezzo surface. The parameter q here might be explained to be such a moduli of elliptic curves as the original surface is recovered to be the limit at the boundary value q = 0. The q-quantization is such a deformation of the surface.Through the investigation of this year, for a general value of q, fundamental geometric invariants of the deformed surface such as the Chern numbers, the Hodge numbers etc. are calculated. This result will give devices for clarifying the mixed Hodge structure of the surface, considering then the Torelli problem to it, and characterising the c-quantisation: in the whole deformatin space. This result was shown by observing a ertain similarity (algebraic correspondence) of the quantization to a Kummer or an abelian surface, so it is also highly expectable that there can be constructed a coherent sheaf of theta-functions over the parameter space of the quantization and that this can be realized as the solution-sheaf of a certain heat equation naturally arising from the space Through, the affirmation of this expectation, one would easily turn back to the original objective in the GBS-theory.

通过前一年的活动证明，椭圆曲面上主单群丛的研究是E型例外群中最有趣的情况，它与Del-Pezzo曲面的Q量子化研究密切相关。这里的参数q可以解释为这样的椭圆曲线的模数，因为原始曲面被恢复为在边界值q=0处的极限。Q量子化就是这样一种表面形变。通过今年的研究，对于一般的Q值，计算了形变表面的基本几何不变量，如陈数、霍奇数等。这一结果将为阐明曲面的混合Hodge结构，然后考虑它的Torelli问题，并刻画整个变形空间中的c-量子化提供了工具。这一结果是通过观察量子化与Kummer或Abel曲面的某种相似性(代数对应)而显示出来的，因此也很有可能在量子化的参数空间上构造一个相干的theta函数束，并且这可以实现为从该空间自然产生的某个热方程的解束。通过这种期望的肯定，人们很容易回到GBS理论的原始目标。