Minimal free resolutions of ideals of minors associated to pairs of matrices
András Cristian Lőrincz
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Submission date: 25. Jan. 2020
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Consider the aﬃne space consisting of pairs of matrices (A,B) of ﬁxed size, and its closed subvariety given by the rank conditions rank A ≤ a, rank B ≤ b and rank(AB) ≤ c, for three non-negative integers a,b,c. These varieties are precisely the orbit closures of representations for the equioriented A3 quiver. In this paper we construct the (equivariant) minimal free resolutions of the deﬁning ideals of such varieties. We show how this problem is equivalent to determining the cohomology groups of the tensor product of two Schur functors of tautological bundles on a 2-step ﬂag variety. We provide several techniques for the determination of these groups, which is of independent interest.