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Projective dimension and Castelnuovo-Mumford regularity of t-spread ideals

Luca Amata, Marilena Crupi, Antonino Ficarra

Abstract

We study some algebraic invariants of $t$-spread ideals, $t\ge 1$, such as the projective dimension and the Castelnuovo-Mumford regularity, by means of well-known graded resolutions. We state upper bounds for these invariants and, furthermore, we identify a special class of t-spread ideals for which such bounds are optimal.

Projective dimension and Castelnuovo-Mumford regularity of t-spread ideals

Abstract

We study some algebraic invariants of -spread ideals, , such as the projective dimension and the Castelnuovo-Mumford regularity, by means of well-known graded resolutions. We state upper bounds for these invariants and, furthermore, we identify a special class of t-spread ideals for which such bounds are optimal.
Paper Structure (5 sections, 11 theorems, 82 equations)

This paper contains 5 sections, 11 theorems, 82 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Projective dimension and regularity
  4. Regularity of $t$--spread ideals
  5. Some Applications

Key Result

Theorem 3.1

EHGB Let $M$ be a finitely generated graded $S$--module, a minimal graded free resolution of $M$ with $F_i=\bigoplus_jS(-j)^{\beta_{i,j}}$, and a graded free $S$--resolution of $M$ with $G_i=\bigoplus_jS(-j)^{\textup{b}_{i,j}}$. Then for all $i$ and $j$.

Theorems & Definitions (27)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Theorem 3.1
  • Example 3.2
  • Theorem 3.3
  • Remark 3.4
  • Example 3.5
  • Example 3.6
  • Theorem 4.1
  • ...and 17 more