The minimal free resolution of fat almost complete intersections in\n \ℙ¹\×\ℙ¹

2016/05/16 by Giuseppe Favacchio, Favacchio, Giuseppe, Elena Guardo +1
Computer Science · Engineering · Mathematics · #13A15 #13C40 #13F20 #14C20 #14M05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1605.04769

openalex publication_date 2016/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A current research theme is to compare symbolic powers of an ideal I with\nthe regular powers of I. In this paper, we focus on the case that I=I_X is\nan ideal defining an almost complete intersection (ACI) sets of points X in\n\ℙ¹\×\ℙ¹. In particular, we describe a minimal free\nbigraded resolution of a non arithmetically Cohen-Macaulay (also non\nhomogeneus) set of fat points mathcal Z whose support is an ACI. We call\n mathcal Z a fat ACI. We also show that its symbolic and ordinary powers are\nequal, i.e, I _{mathcal Z}^(m)=I _{mathcal Z}^m for any m\≥ 1.\n

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