Tight closure and continuous closure

TL;DR

This paper proves that in certain algebraic settings over complex numbers, the tight closure of primary ideals is always contained within their continuous closure, linking two important closure operations.

Contribution

It establishes a containment relationship between tight closure and continuous closure for primary ideals in normal domains over complex numbers.

Findings

Tight closure is contained in continuous closure for primary ideals.

The result applies to normal domains of finite type over complex numbers.

Provides a new connection between algebraic and analytic closure operations.

Abstract

We show that for ideals primary to a maximal ideal in a normal domain of finite type over the complex numbers, its tight closure is contained inside the continuous closure.