Asymptotic invariants of ideals with Noetherian symbolic Rees algebra and applications to cover ideals

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Drabkin, Benjamin¹  Guerrieri, Lorenzo² 

[1] Univ Nebraska, Lincoln, NE 68588 USA

[2] Univ Catania, Dipartimento Matemat & Informat, Viale A Doria 6, I-95125 Catania, Italy

关键词: Symbolic powers;    Symbolic defect;    Waldschimdt constant;    Monomial ideals;    Cover ideals of graphs;   

DOI  :  10.1016/j.jpaa.2019.05.008

来源: Elsevier

【 摘 要 】

Let I be an ideal whose symbolic Rees algebra is Noetherian. For m >= 1, the m-th symbolic defect, sdefect(I, m), of I is defined to be the minimal number of generators of the module I-(m)/I-(m). We prove that sdefect(I, m) is eventually quasi-polynomial as a function in m. We compute the symbolic defect explicitly for certain monomial ideals arising from graphs, termed cover ideals. We go on to give a formula for the Waldschmidt constant, an asymptotic invariant measuring the growth of the degrees of generators of symbolic powers, for ideals whose symbolic Rees algebra is Noetherian. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free