MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Minimal free resolutions of ideals of minors associated to pairs of matrices

András Cristian Lőrincz


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 $\leq$ a, rank B $\leq$ b and rank(A⋅B) $\leq$ c, for three non-negative integers a,b,c. These varieties are precisely the orbit closures of representations for the equioriented $A_3$ 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.


Related publications

2021 Repository Open Access
András Christian Lőrincz

Minimal free resolutions of ideals of minors associated to pairs of matrices

In: Proceedings of the American Mathematical Society, 149 (2021) 5, pp. 1857-1873