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Admissible态射和tubular型加权射影线的凝聚层范畴

2020-12-02阅读(243)

Admissible态射和tubular型加权射影线的凝聚层范畴

论文摘要

加权射影线由射影直线P1（k）中t个两两不同的数构成的有序数列λ =（λ1,λ2,…,λt）和权序列p=（p1,p2,…,pt）构成,记为X（p,λ）.权序列确定一个秩为1的阿贝尔群L（p）,称为string群.加权射影线X（p,λ）确定L（p）-分次的齐次坐标代数S（p,λ）.加权射影线的凝聚层范畴coh-X（p,λ）是L（p）分次S（p,λ）-有限生成模范畴模去L（p）分次S（p,λ）-有限维模范畴的商范畴.为研究不同的加权射影线的凝聚层范畴之间的关系,文[1]定义了string群之间的admissible态射.利用admissible态射nπ:L（p）→ L（q）,可导出范畴等价（coh-X（p,λ））kerπ→coh-X（q,μ）.其中（coh-X（p,λ））kerπ是群kerπ导出的等变范畴.本论文研究tubular型的string群之间的admissible态射.第一章回顾了加权射影线的凝聚层范畴的发展历史,介绍了本论文的背景.第二章回顾了相关的基础知识.第三章给出了tubular型的admissible态射的完全分类.第四章刻画了由admissible态射确定的tubular型的加权射影线的凝聚层范畴之间的联系.

论文目录

  • 中文摘要
  • abstract
  • 第一章 综述
  • 第二章 Admissible态射
  •   2.1 加权射影线的凝聚层范畴和齐次坐标代数
  •   2.2 Admissible态射
  •   2.3 群作用和等变范畴
  • 第三章 Tubular型的admissible态射的分类
  • 第四章 Tubular型的加权射影线的凝聚层范畴之间的联系
  • 1）)和coh-X（2,2,2,2;λ2）之间的关系'>  4.1 coh-X（2,2,2,2;λ1）)和coh-X（2,2,2,2;λ2）之间的关系
  •   4.2 coh-X（4,4,2）和coh-X（2,2,2,2;λ）之间的关系
  •   4.3 coh-X（6,3,2）和coh-X（2,2,2,2;λ）之间的关系
  •   4.4 coh-X（6,3,2）和coh-X（3,3,3）之间的关系
  •   4.5 coh-X（4,4,2）和coh-X（4,4,2）之间的关系
  •   4.6 coh-X（3,3,3）和coh-X（3,3,3）之间的关系
  • 参考文献
  • 致谢

    • 文章来源

    类型: 硕士论文

    作者: 张洪侠

    导师: 林亚南

    关键词: 加权射影线,齐次坐标代数,凝聚层范畴,态射

    来源: 厦门大学

    年度: 2019

    分类: 基础科学

    专业: 数学

    单位: 厦门大学

    分类号: O154.1

    总页数: 36

    文件大小: 1465K

    下载量: 4

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