Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix

Autor:	Gesmundo, Fulvio, Hang, Huang, Schenck, Hal, Weyman, Jerzy
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Mathematics - Algebraic Geometry 13D02 13F55 13C40 68Q15
Druh dokumentu:	Working Paper
Popis:	We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither prime nor Cohen-Macaulay. We combine work of Laubenbacher-Swanson on the Gr\"obner basis of an ideal of $2 \times 2$ permanents of a generic matrix with our previous work connecting the initial ideal of $2 \times 2$ permanents to a simplicial complex. The main technical tool is a spectral sequence arising from the Bernstein-Gelfand-Gelfand correspondence. Comment: 24 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.12247 Zobrazit plný text záznamu View this record from Arxiv