The $\tau$-invariant and elimination

TL;DR

This paper investigates the properties of the $ au$-invariant in Rees algebras, demonstrating its favorable behavior under integral closure and variable elimination processes.

Contribution

It provides new results on the stability of the $ au$-invariant during integral closure and elimination in Rees algebras.

Findings

$ au$-invariant remains stable under integral closure

Good behavior of $ au$-invariant during elimination

Enhances understanding of Rees algebra invariants

Abstract

In this paper we present some results showing the good behavior of the $\tau$-invariant of a Rees algebra with integral closure and elimination (of variables).