# Regularity bounds for twisted commutative algebras

## TL;DR

This paper establishes bounds on the regularity of modules over twisted commutative algebras, extending previous results from the case of a single generator to multiple generators.

## Contribution

It generalizes the regularity bounds for twisted commutative algebras from one generator to multiple generators, providing a broader understanding of their module resolutions.

## Key findings

- Regularity of A-modules can be bounded by the first floor(d^2/4)+2 terms of their minimal free resolution.
- Extends previous results from the case d=1 to arbitrary d.
- Provides new bounds applicable to a wider class of twisted commutative algebras.

## Abstract

Let A be the twisted commutative algebra freely generated by d indeterminates of degree 1. We show that the regularity of an A-module can be bounded from the first floor(d^2/4) + 2 terms of its minimal free resolution. This extends results of Church and Ellenberg from the d=1 case.