The Minimal Free Resolution of A Star-Configuration in ℙⁿ

2014/04/18 by Jung Pil Park, Park, Jung Pil, Yong-Su Shin +1
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Point processes and geometric inequalities #Primary:13A02 #Secondary:16W50

paper · pdf · doi:10.48550/arxiv.1404.4724

openalex publication_date 2014/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the minimal free resolution of the ideal of a star-configuration in ℙⁿ of type (r,s) defined by general forms in R=\Bbbk[x₀,x₁,…,x_n]. This generalises the results of \citeAS:1,GHM from a specific value of r=2 to any value of 1≤ r≤ n. Moreover, we show that any star-configuration in ℙⁿ is arithmetically Cohen-Macaulay. As an application, we construct a few of graded Artinian rings, which have the weak Lefschetz property, using the sum of two ideals of star-configurations in ℙⁿ.

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