A lower bound on levels with applications to Koszul Complexes

TL;DR

This paper establishes an optimal lower bound on the level of perfect complexes with torsion homology, improving bounds for Koszul complexes and providing practical examples.

Contribution

It introduces a new lower bound for the level of perfect complexes with torsion homology and applies it to enhance bounds on Koszul complexes.

Findings

Bound is proven to be optimal with examples.

Improved lower bounds for Koszul complexes on various sequences.

Applications demonstrate the bound's effectiveness.

Abstract

In this paper, we establish a lower bound on the level of a perfect complex with power torsion homology on positive degrees and a power torsion minimal generator for zero homology. Examples are provided to demonstrate that the bound is optimal. This result is applied to improve existing lower bounds on the level of a Koszul complex on various classes of sequences.