Non-commutative desingularization of determinantal varieties I

• 成果类型: Article
• 署名作者: Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; Van den Bergh, Michel
• 署名单位: Syracuse University; University of Toronto; University Toronto Scarborough; Hasselt University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0258-7
• 发表日期: 2010
• 页码: 47-115
• 关键词: modules

摘要

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.