Comparing the commutative and non-commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices

TL;DR

This paper explores the relationship between non-commutative and classical resolutions of determinantal varieties of symmetric and skew-symmetric matrices, establishing a full faithful embedding between their derived categories.

Contribution

It constructs a full faithful embedding linking the derived categories of non-commutative and Springer resolutions for these determinantal varieties.

Findings

Established a categorical embedding between resolutions

Bridged non-commutative and classical geometric approaches

Enhanced understanding of derived categories for determinantal varieties

Abstract

Let Y be the variety of (skew) symmetric nxn-matrices of rank less than or equal to r. In paper we construct a full faithful embedding between the derived category of a non-commutative resolution of Y, constructed earlier by the authors, and the derived category of the classical Springer resolution of Y.