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arXiv · 1909.11705

Relations between the 2x2 minors of a generic matrix

Hang Huang·Michael Perlman·Claudia Polini·Claudiu Raicu·Alessio Sammartano
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Abstract

We prove the case t = 2 of a conjecture of Bruns-Conca-Varbaro, describing the minimal relations between the t x 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 x 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).

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Hang Huang, Michael Perlman, Claudia Polini, Claudiu Raicu, Alessio Sammartano. 2019-09-25. Relations between the 2x2 minors of a generic matrix. https://doi.org/10.1016/j.aim.2021.107807

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