Relations between the 2x2 minors of a generic matrix
2019
We prove a conjecture of Bruns-Conca-Varbaro, describing the minimal relations between the 2x2 minors of a generic matrix. Interpreting these relations as polynomial functors, and applying transpose duality as in the work of Sam-Snowden, this problem is equivalent to understanding the relations satisfied by 2x2 generalized permanents. Our proof follows by combining Koszul homology calculations on the minors side, with a study of subspace varieties on the permanents side, and with the Kempf-Weyman technique (on both sides).
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