Special tight closure

TL;DR

This paper introduces the concept of special tight closure in normal rings, showing that the tight closure of an ideal can be decomposed into the ideal itself plus a specific component called the special tight closure.

Contribution

It establishes a new decomposition of tight closure in normal rings, providing a clearer understanding of its structure and computation.

Findings

Tight closure in normal rings can be expressed as the sum of the ideal and the special tight closure.

The special tight closure is a distinct component that aids in understanding the overall tight closure.

The decomposition simplifies calculations and theoretical analysis of tight closure in algebraic geometry.

Abstract

We prove that in normal rings the tight closure of an ideal can be computed as the sum of the ideal and a piece of the tight closure, called the special tight closure.