Virtual resolutions of points in ℙ¹ × ℙ¹

2021/06/05 by Megumi Harada, Harada, Megumi, Maryam Nowroozi +3
Computer Science · Mathematics · #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary: 13D02 #Secondary: 14M05

paper · pdf · doi:10.48550/arxiv.2106.02759

openalex publication_date 2021/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore explicit virtual resolutions, as introduced by Berkesch, Erman, and Smith, for ideals of sets of points in ℙ¹ × ℙ¹. Specifically, we describe a virtual resolution for a sufficiently general set of points X in ℙ¹ × ℙ¹ that only depends on |X|. We also improve an existence result of Berkesch, Erman, and Smith in the special case of points in ℙ¹ × ℙ¹; more precisely, we give an effective bound for their construction that gives a virtual resolution of length two for any set of points in ℙ¹ × ℙ¹.

Related

• Hilbert-Burch virtual resolutions for points in ℙ¹×ℙ¹
• On virtual resolutions of points in a product of projective spaces
• Virtual Complete Intersections in ℙ¹ × ℙ¹
• Gale Duality and Free Resolutions of Ideals of Points
• Resolutions of Subsets of Finite Sets of Points in Projective Space