Non-commutative desingularization of determinantal varieties I

Ragnar Olaf Buchweitz; Graham J. Leuschke; Michel van den Bergh

doi:10.1007/s00222-010-0258-7

Non-commutative desingularization of determinantal varieties I

Ragnar Olaf Buchweitz, Graham J. Leuschke, Michel van den Bergh

Department of Mathematics

Research output: Contribution to journal › Article

16 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	47-115
Number of pages	69
Journal	Inventiones Mathematicae
Volume	182
Issue number	1
DOIs	https://doi.org/10.1007/s00222-010-0258-7
State	Published - Jun 8 2010

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00222-010-0258-7

Fingerprint Dive into the research topics of 'Non-commutative desingularization of determinantal varieties I'. Together they form a unique fingerprint.

Cite this

Buchweitz, R. O., Leuschke, G. J., & van den Bergh, M. (2010). Non-commutative desingularization of determinantal varieties I. Inventiones Mathematicae, 182(1), 47-115. https://doi.org/10.1007/s00222-010-0258-7

@article{1f8850f67910437db754da34549a56cd,

title = "Non-commutative desingularization of determinantal varieties I",

abstract = "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.",

author = "Buchweitz, {Ragnar Olaf} and Leuschke, {Graham J.} and {van den Bergh}, Michel",

year = "2010",

month = jun,

day = "8",

doi = "10.1007/s00222-010-0258-7",

language = "English (US)",

volume = "182",

pages = "47--115",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Non-commutative desingularization of determinantal varieties I

AU - Buchweitz, Ragnar Olaf

AU - Leuschke, Graham J.

AU - van den Bergh, Michel

PY - 2010/6/8

Y1 - 2010/6/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955304031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955304031&partnerID=8YFLogxK

U2 - 10.1007/s00222-010-0258-7

DO - 10.1007/s00222-010-0258-7

M3 - Article

AN - SCOPUS:77955304031

VL - 182

SP - 47

EP - 115

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 1

ER -