Tilting bundles and the missing part on a weighted projective line of type (2, 2, n)
Tilting bundles and the missing part on a weighted projective line of type (2, 2, n)
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(2, 2, n) 型加权投影线上的倾斜束和缺失部分
DOI：
10.1016/j.jpaa.2014.09.015
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发表时间：
2015
影响因子：
0.8
通讯作者：
Ruan Shiquan
中科院分区：
文献类型：
--
作者：
Chen Jianmin;Lin Yanan;Ruan Shiquan
本文研究了（2,2,n）型加权投影线上相干束的倾斜束，即矢量束倾斜束。我们将所有的倾斜束分为两类，一类包含由线束组成的倾斜束，另一类包含有不可分解和的倾斜束，这些和不是线束。此外，对于每一个倾斜束T（具有自同态代数Λ），我们证明了从相干束范畴到有限生成右范畴Λ-modules的缺失部分都带有一个阿贝尔范畴的结构。
This paper is devoted to investigate the tilting bundles, ie tilting sheaves that are vector bundles, in the category of coherent sheaves on a weighted projective line of type (2, 2, n). We classify all the tilting bundles into two classes, one containing the tilting bundles that are consisting of line bundles, and the other one containing tilting bundles with indecomposable summands that are not line bundles. Moreover, for each tilting bundle T (with endomorphism algebra Λ) we prove that the missing part, from the category of coherent sheaves to the category of finitely generated right Λ-modules, carries the structure of an abelian category.