We prove the case t = 2 of a conjecture of Bruns–Conca– Varbaro, describing the minimal relations between the t × t 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 t × t 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).
Relations between the 2x2 minors of a generic matrix
A. Sammartano
2021-01-01
Abstract
We prove the case t = 2 of a conjecture of Bruns–Conca– Varbaro, describing the minimal relations between the t × t 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 t × t 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).File in questo prodotto:
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