Mixed Hodge Structures on the rational homotopy type of intersection spaces

TL;DR

This paper demonstrates that the rational cohomology of perverse intersection spaces associated with certain complex projective varieties can be equipped with compatible mixed Hodge structures, enriching their geometric understanding.

Contribution

It introduces a method to endow the rational cohomology of intersection spaces with compatible mixed Hodge structures for varieties with isolated singularities.

Findings

Rational cohomology of intersection spaces admits mixed Hodge structures.

Compatibility of these structures across the family of perverse intersection spaces.

Applicable to complex projective varieties with simply connected links.

Abstract

Let $X$ a complex projective variety of complex dimension $n$ with only isolated singularities of simply connected links. We show that we can endow the rational cohomology of the family of the $\overline{p}$-perverse intersection spaces $\{ I^{\overline{p}}X \}$ with compatible mixed Hodge structures.