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

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

2012-04-02

arxiv.org/abs/1204.0488v1

Mathematics

Algebraic Geometry

40 pages

Scientific paper

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.

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