Relations between the 2x2 minors of a generic matrix
Commutative Algebra
2021-06-04 v2
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).
Keywords
Cite
@article{arxiv.1909.11705,
title = {Relations between the 2x2 minors of a generic matrix},
author = {Hang Huang and Michael Perlman and Claudia Polini and Claudiu Raicu and Alessio Sammartano},
journal= {arXiv preprint arXiv:1909.11705},
year = {2021}
}
Comments
21 pages. To appear in Advances in Mathematics