Local Cohomological Defect and a Conjecture of Mustata-Popa

TL;DR

This paper establishes a general result on the depth of Du Bois complexes for singular varieties, confirming a conjecture of Mustata-Popa and extending previous results on local cohomological defects.

Contribution

It proves a new general theorem on Du Bois complexes and applies it to verify a conjecture, advancing understanding of local cohomological defects in algebraic geometry.

Findings

Proved a general result on the depth of Du Bois complexes.

Confirmed the Mustata-Popa conjecture.

Extended results on local cohomological defect over complex numbers.

Abstract

We prove a general result on the depth of Du Bois complexes of a singular variety. We apply it to prove a conjecture of Mustata-Popa and to study the local cohomological defect, extending results of Ogus and Dao-Takagi over the complex numbers.