Tight closure of products and F-rational singularities

TL;DR

This paper characterizes F-rationality through tight closure of parameter ideals' products, extending classical surface singularity results to higher dimensions using algebraic closure techniques.

Contribution

It introduces a new characterization of F-rationality based on tight closure of products of parameter ideals, generalizing surface singularity theories to higher dimensions.

Findings

F-rationality characterized by tight closure of parameter ideals' products

Extension of surface singularity results to higher dimensions

Connection between algebraic closure and singularity classification

Abstract

We prove a characterization of F-rationality in terms of tight closure of products of parameter ideals. Our results are inspired by the theory of complete ideals for surfaces and, in particular, the fundamental results of Lipman-Teissier and Cutkosky characterizing rational surface singularities in terms of products of complete ideals, but are valid also in higher dimensions.