Noncommutative desingularization of orbit closures for some representations of $GL_n$

Jerzy Weyman; Gufang Zhao

Noncommutative desingularization of orbit closures for some representations of $GL_n$

Algebraic Geometry 2019-11-21 v3 Commutative Algebra Representation Theory

Authors: Jerzy Weyman , Gufang Zhao

Abstract

We describe noncommutative desingularizations of determinantal varieties, determinantal varieties defined by minors of generic symmetric matrices, and pfaffian varieties defined by pfaffians of generic anti-symmetric matrices. For maximal minors of square matrices and symmetric matrices, this gives a non-commutative crepant resolution. Along the way, we describe a method to calculate the quiver with relations for any non-commutative desingularizations coming from exceptional collections over partial flag varieties.

Keywords

noncommutative desingularization determinantal varieties pfaffian varieties non-commutative crepant resolution orbit closures quiver with relations exceptional collections

Cite

@article{arxiv.1204.0488,
  title  = {Noncommutative desingularization of orbit closures for some representations of $GL_n$},
  author = {Jerzy Weyman and Gufang Zhao},
  journal= {arXiv preprint arXiv:1204.0488},
  year   = {2019}
}

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Significant revisions, 39 pages

Noncommutative desingularization of orbit closures for some representations of $GL_n$

Abstract

Keywords

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