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The syzygies of some thickenings of determinantal varieties Raicu, Claudiu


The space of \(m \times n\) matrices admits a natural action of the group \(GL_m \times GL_n\) via row and column operations on the matrix entries. The invariant closed subsets are the determinantal varieties defined by the (reduced) ideals of minors of the generic matrix. The minimal free resolutions of these ideals are well-understood by work of Lascoux and others. There are however many more invariant ideals which are non-reduced, and they were classified by De Concini, Eisenbud and Procesi in the 80s. I will explain how to determine the syzygies of a large class of these ideals by employing a surprising connection with the representation theory of general linear Lie superalgebras. This is joint work with Jerzy Weyman.

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