Noncommutative desingularization of orbit closures for some representations of $G{L}_n$

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.

Significant revisions, 39 pages

References in corpus (5)

• Noncommutative Counterparts of the Springer Resolution
• Non-commutative desingularization of determinantal varieties, I
• Pieri resolutions for classical groups
• Non-commutative desingularization of determinantal varieties, II: Arbitrary minors
• Hochschild (Co-)Homology of Schemes with Tilting Object

Cited by in corpus (3)

• Non-commutative resolutions of quotient singularities
• Categorification via blocks of modular representations for sl(n)
• On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions