Resurgence and Castelnuovo-Mumford regularity of certain monomial curves in \mathbb A³

2019/04/11 by Clare D’Cruz, D'Cruz, Clare
Mathematics · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1904.05797

Abstract

Let \mathfrak p be the defining ideal of the monomial curve \mathcal C(2q+1, 2q+1+m, 2q+1+2m) in the affine space \mathbb A_k³ parameterized by (x^{2q +1}, x^{2q +1 + m}, x^{2q +1 +2 m}) where gcd( 2q+1,m)=1. In this paper we compute the resurgence of \mathfrak p, the Waldschmidt constant of \mathfrak p and the Castelnuovo-Mumford regularity of the symbolic powers of \mathfrak p.

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