2016/10/12 by Clare D’Cruz, D'Cruz, Clare, Shreedevi K. Masuti +1
Computer Science · Mathematics · #1305 #13A30 #13H15 #13P10 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1610.03658
openalex publication_date 2016/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let d \≥ 2 and m\≥ 1 be integers such that \gcd (d,m)=1. Let\n mathfrak p be the defining ideal of the monomial curve in mathbb A_\n Bbbkkd parametrized by (tn1, \…, tnd) where ni = d +\n(i-1)m for all i = 1, \…, d. In this paper, we describe the symbolic\npowers mathfrak p(n) for all n \≥ 1. As a consequence we show that\nthe symbolic blowup algebras mathcal Rs( mathfrak p) and\nGs( mathfrak p) are Cohen-Macaulay. This gives a positive answer to a\nquestion posed by S.~Goto in citegoto. We also discuss when these blowup\nalgebras are Gorenstein. Moreover, for d=3, considering mathfrak p as a\nweighted homogeneous ideal, we compute the resurgence, the Waldschmidt constant\nand the Castelnuovo-Mumford regularity of mathfrak p(n) for all n \≥\n1. The techniques of this paper for computing mathfrak p(n) are new\nand we hope that these will be useful to study the symbolic powers of other\nprime ideals.\n