Characterization and finite descent of local cohomological invariants

TL;DR

This paper introduces simplified characterizations of certain local cohomological invariants of varieties and demonstrates their descent properties under finite surjective morphisms, advancing understanding of their behavior.

Contribution

It provides new left-inverse characterizations of singularity invariants and proves their descent under finite morphisms, enhancing their applicability.

Findings

Simplified characterizations of invariants $c(Z)$, $w(Z)$, and ${ m HRH}(Z)$.

Establishment of descent results for these invariants.

Application of trace morphism to prove descent properties.

Abstract

We provide simple ``left-inverse characterizations'' of the recently introduced singularity invariants $c(Z)$, $w(Z)$, and ${\rm HRH}(Z)$ of an equidimensional variety $Z$. Combining this with a trace morphism, we establish descent results of these invariants for finite surjective morphisms.