The full exceptional collections of categorical resolutions of curves

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:220

Article

Wei, Zhaoting¹ 

[1] Indiana Univ, Dept Math, 831 E 3rd St, Bloomington, IN 47405 USA

关键词: Categorical resolution;    Singular curve;    K-theory;    Exceptional collection;    Tilting object;   

DOI  :  10.1016/j.jpaa.2016.02.018

来源: Elsevier

【 摘 要 】

This paper gives a complete answer of the following question: which (singular, projective) curves have a categorical resolution of singularities which admits a full exceptional collection? We prove that such full exceptional collection exists if and only if the geometric genus of the curve equals to 0. Moreover we can also prove that a curve with geometric genus equal or greater than 1 cannot have a categorical resolution of singularities which has a tilting object. The proofs of both results are given by a careful study of the Grothendieck group and the Picard group of that curve. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free