Infinitesimal Automorphisms of Algebraic Varieties

代数簇的无穷小自同构

• 批准号: 424830165
• 负责人: Dr. Gebhard Martin
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/424830165?language=en
• 关键词: Infinitesimal; Automorphisms; Algebraic; Varieties

The purpose of this project is to study the automorphism scheme of smooth projective varieties in positive characteristic. In this context, infinitesimal automorphisms, i.e. subgroup schemes of the automorphism scheme which are contained in an infinitesimal neighborhood of the identity, play a fundamental role. This is in stark contrast to the situation in characteristic 0 where such non-reduced group schemes do not even exist. The first part of this project will be the explicit calculation of infinitesimal automorphisms in the case of non-ruled surfaces of special type and the construction of varieties of higher dimension, such as Calabi-Yau threefolds, using the results of these computations. In the second part, I want to study the scheme structure of the group scheme of automorphisms of surfaces and varieties of general type along with their canonical models from a more abstract perspective and work towards giving a bound on the length of this automorphism scheme.

本课题的目的是研究具有正特征的光滑射影簇的自同构方案。在这种情况下，无穷小自同构，即包含在单位元的无穷小邻域中的自同构方案的子群方案，起着基本的作用。这与特征0中的情况形成鲜明对比，在特征0中甚至不存在这样的非约化群方案。这个项目的第一部分将是显式计算无穷小自同构的情况下，非直纹曲面的特殊类型和建设品种的高维，如卡-丘三倍，使用这些计算的结果。在第二部分中，我想从一个更抽象的角度研究一般类型的曲面和变种的自同构的群方案沿着规范模型的方案结构，并努力给出这个自同构方案的长度的界。