# An Eisenbud-Goto-type Upper Bound for the Castelnuovo-Mumford Regularity of Fake Weighted Projective Spaces

## TL;DR

This paper establishes an Eisenbud-Goto-type upper bound for the Castelnuovo-Mumford regularity of certain projective toric varieties, specifically focusing on very ample lattice simplices and fake weighted projective spaces.

## Contribution

It introduces a new upper bound for the regularity of specific classes of projective toric varieties, extending Eisenbud-Goto bounds to fake weighted projective spaces.

## Key findings

- Upper bound for the $k$-normality of very ample lattice simplices
- Eisenbud-Goto-type bound for certain projective toric varieties
- Application to fake weighted projective spaces

## Abstract

We will give an upper bound for the $k$-normality of very ample lattice simplices, and then give an Eisenbud-Goto-type bound for some special classes of projective toric varieties.