A bound on the Hodge filtration of the de Rham cohomology of supervarieties

TL;DR

This paper investigates the relationship between the Hodge filtration of de Rham cohomology in supervarieties and their reduced counterparts, providing insights into their structural connections.

Contribution

It establishes a bound on the Hodge filtration of supervarieties' de Rham cohomology relative to the classical case, advancing understanding of supergeometry.

Findings

Derived a bound relating supervariety and reduced variety filtrations

Connected supergeometry with classical Hodge theory

Enhanced understanding of supervarieties' cohomological properties

Abstract

We study the relation between the Hodge filtration of the de Rham cohomology of a proper smooth supervariety $X$ and the usual Hodge filtration of the corresponding reduced variety $X_0$.