Rational homotopy and intersection-formality of complex algebraic varieties

Abstract

A homotopical treatment of intersection cohomology recently developed by Chataur–Saralegui–Tanre associates a perverse algebraic model to every topological pseudomanifold, extending Sullivan’s presentation of rational homotopy theory to intersection cohomology. In this context, there is a notion of intersection-formality, measuring the vanishing of higher Massey products in intersection cohomology. In the present paper, we study the perverse algebraic model of complex projective varieties with isolated singularities. We then use mixed Hodge theory to prove some intersection-formality results for large families of complex projective varieties, such as isolated surface singularities and varieties of arbitrary dimension with ordinary isolated singularities.