Hilbert-Burch virtual resolutions for points in $\mathbb{P}^1\times\mathbb{P}^1$

Autor:	Booms-Peot, Caitlyn
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Mathematics - Algebraic Geometry 13D02 (Primary) 14M25 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Building off of work of Harada, Nowroozi, and Van Tuyl which provided particular length two virtual resolutions for finite sets of points in $\mathbb{P}^1\times\mathbb{P}^1$, we prove that the vast majority of virtual resolutions of a pair for minimal elements of the multigraded regularity in this setting are of Hilbert-Burch type. We give explicit descriptions of these short virtual resolutions that depend only on the number of points. Moreover, despite initial evidence, we show that these virtual resolutions are not always short, and we give sufficient conditions for when they are length three. Comment: 21 pages, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.04953 Zobrazit plný text záznamu View this record from Arxiv