不同权型加权射影线的关联与转化

本项目研究不同权型加权射影线的关联与转化，内容包括：(1)考察orbifold商观点下不同权型加权射影线的关联；(2)讨论加权射影线的凝聚层范畴在群作用下的等变转化；(3)探索加权射影线凝聚层导出范畴上的Frobenius-Perron理论；(4)如上研究的高维推广。项目的预期目标是：(1)建立orbifold商观点下tubular型加权射影线的完全关联及wild型加权射影线的部分关联；(2)具体刻画加权射影线的凝聚层范畴在群作用下的等变转化；(3)利用Frobenius-Perron维数及相关不变量对加权射影线特别是wild型加权射影线进行精细分类；(4)实现不同权型Geigle-Lenzing射影空间的关联与转化。本项目是国际前沿的多学科交叉研究，是多视角多方法的创新探索。

This project focuses on studying the correlations and transforms of weighted projective lines with different weight types, including: (1)investigating the correlations of weighted projective lines as the orbifold quotients of Riemann surfaces; (2)discussing the equivariant relationships between the categories of coherent sheaves over weighted projective lines under group actions; (3)exploring the Frobenius-Perron theory on the derived categories of coherent sheaves over weighted projective lines; (4)extending the above studies to higher dimensional forms of weighted projective lines. The expectations are: (1)establishing the links of weighted projective lines with different weight types in term of orbifold quotients; (2)providing the transforms of the categories of coherent sheaves over weighted projective lines through group actions specifically; (3)classifying the weighted projective lines, especially the weighted projective lines of wild types, by using Frobenius-Perron dimension and related invariants; (4)describing the correlations and transforms of Geigel-Lenzing projective spaces. This project is an interdisciplinary research of international frontier. It is an innovative exploration of multi-perspective and multi-method.