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

TL;DR

This paper investigates algebraic invariants like projective dimension and Castelnuovo-Mumford regularity of t-spread ideals, providing bounds and identifying cases where these bounds are tight.

Contribution

It introduces bounds for these invariants of t-spread ideals and characterizes a class where these bounds are achieved.

Findings

Established upper bounds for projective dimension and regularity of t-spread ideals.

Identified a special class of t-spread ideals with optimal bounds.

Provided insights into the graded resolutions of t-spread ideals.

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.