Lower bound for the regularity index of fat points

TL;DR

This paper establishes a lower bound for the regularity index of fat points, aiding in the determination of this invariant which has been primarily studied for upper bounds.

Contribution

It introduces a novel lower bound for the regularity index of fat points, complementing existing upper bound results.

Findings

Provides a new lower bound for the regularity index

Enhances understanding of the regularity index's behavior

Facilitates more accurate determination of the regularity index

Abstract

The problem to find an upper bound for the regularity index of fat points has been dealt with by many authors. In this paper we give a lower bound for the regularity index of fat points. It is useful for determining the regularity index.