Symbolic Powers of Derksen Ideals

TL;DR

This paper investigates conditions under which symbolic and ordinary powers of Derksen ideals, associated with finite group actions on polynomial rings, are equal for all natural numbers.

Contribution

It provides new criteria for the equality of symbolic and ordinary powers specifically for Derksen ideals under finite group actions.

Findings

Identifies conditions ensuring symbolic and ordinary powers coincide.

Establishes results for Derksen ideals in the context of finite group actions.

Contributes to understanding the algebraic structure of Derksen ideals.

Abstract

Given that symbolic and ordinary powers of an ideal do not always coincide, we look for conditions on the ideal such that equality holds for every natural number. This paper focuses on studying the equality for Derksen ideals defined by finite groups acting linearly on a polynomial ring.