Mixed Hodge Structures on the rational homotopy type of intersection spaces

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.

47 pages