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.
Rational homotopy of complex projective varieties with normal isolated singularities
On the rational homotopy type of intersection spaces
Rational homotopy type of mapping spaces via cohomology algebras
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