厦门大学学报（自然科学版）2023，Vol.62Issue(6)：937-947,11.DOI:10.6043/j.issn.0438-0479.202305008
加权射影线上的倾斜理论
On tilting theory over weighted projective lines
摘要
Abstract
In this paper,we summarize some of our works on the tilting theory in the category of coherent sheaves over weighted projective lines.Primarily,our summary is divided into three parts:(1)investigating the structure of the"missing part"from the category of coherent sheaves on a weighted projective line to the category of finitely generated right modules on the associated canonical algebra,and proving that,for the weighted projective line of type(2,2,n),the"missing part"carries an abelian structure;(2)finding a canonical tilting object for the stable category of vector bundles on a weighted projective line of type(2,2,2,2),and showing that there does not exist any tilting object consisting only of vector bundles of rank two such that its endomorphism algebra is a canonical algebra;(3)based on the cluster tilting theory,constructing tubular tilting objects in the stable category of vector bundles on a weighted projective line of weight triple and genus one,and classifying the endomorphism algebras of tilting objects in the category of coherent sheaves on a weighted projective line of type(2,2,2,2)and the associated bounded derived category.关键词
加权射影线/凝聚层范畴/倾斜对象/典范代数/丛范畴Key words
weighted projective line/the category of coherent sheaves/tilting object/canonical algebra/cluster category分类
数理科学引用本文复制引用
陈健敏,林亚南,阮诗佺..加权射影线上的倾斜理论[J].厦门大学学报（自然科学版）,2023,62(6):937-947,11.基金项目
国家自然科学基金(11971398,11871404,12271448) （11971398,11871404,12271448）
