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Some inequalities regarding the regularity of powers of monomial ideals

S. A. Seyed Fakhari

Abstract

We prove some inequalities regarding the Castelnuovo--Mumford regularity of symbolic powers and integral closure of powers of monomial ideals.

Some inequalities regarding the regularity of powers of monomial ideals

Abstract

We prove some inequalities regarding the Castelnuovo--Mumford regularity of symbolic powers and integral closure of powers of monomial ideals.
Paper Structure (4 sections, 11 theorems, 51 equations)

This paper contains 4 sections, 11 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Symbolic powers
  4. Integral closure of powers

Key Result

Lemma 2.1

Let $I$ be a monomial ideal in $S$. Then where $\Delta_{\rm\bf a}(I):=\Delta(\sqrt{I: {\rm\bf x^a}})$.

Theorems & Definitions (21)

  • Lemma 2.1: mnptv, Lemmata 2.8 and 2.13
  • Theorem 2.2
  • proof
  • Theorem 3.1
  • proof
  • Corollary 3.2
  • Corollary 3.3
  • proof
  • Lemma 4.1
  • proof
  • ...and 11 more