  A homotopical treatment of intersection cohomology recently developed by
Chataur-Saralegui-Tanr\'e associates a "perverse algebraic model" to every
topological pseudomanifold, extending Sullivan's presentation of rational
homotopy to intersection cohomology. In this context, there is a notion of
"intersection-formality", measuring the vanishing of Massey products in
intersection cohomology. In the present paper, we study the perverse algebraic
model of complex projective varieties with isolated singularities. We endow
such invariant with natural mixed Hodge structures. This allows us 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.
