Non-integrality of integrable over K\"ahler differential forms

TL;DR

This paper demonstrates that for certain singularities, the module of square-integrable top-degree differential forms is not algebraically integral over the K"ahler differential forms, linking to the Nash transform's fiber dimension.

Contribution

It reveals a non-integrality property of square-integrable differential forms over K"ahler forms in singularities, connecting to the Nash transform's fiber dimension.

Findings

Square-integrable forms are not integral over K"ahler forms in certain singularities.

The non-integrality relates to the fiber dimension of the Nash transform.

Provides insight into the structure of differential forms on singular spaces.

Abstract

We show that for a normal isolated singularity the module of square-integrable regular differential forms of top degree is not integral over the module of K\"ahler differential forms. This is related to the fibre dimension of the Nash transform.