Castelnuovo-Mumford regularity of seminormal simplicial affine semigroup rings

TL;DR

This paper proves the Eisenbud-Goto conjecture for seminormal simplicial affine semigroup rings, establishes an upper bound for their Castelnuovo-Mumford regularity, and explicitly computes the regularity of full Veronese rings.

Contribution

It extends the understanding of Castelnuovo-Mumford regularity to seminormal simplicial affine semigroup rings, including explicit calculations for Veronese rings.

Findings

Eisenbud-Goto conjecture holds for seminormal simplicial affine semigroup rings

An upper bound for regularity similar to the normal case is established

Explicit regularity computation for full Veronese rings

Abstract

We show that the Eisenbud-Goto conjecture holds for (homogeneous) seminormal simplicial affine semigroup rings. Moreover, we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the normal case. Finally, we compute explicitly the regularity of full Veronese rings.