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A homotopical treatment of intersection cohomology recently developed byChataur-Saralegui-Tanr\'e associates a "perverse algebraic model" to everytopological pseudomanifold, extending Sullivan's presentation of rationalhomotopy to intersection cohomology. In this context, there is a notion of"intersection-formality", measuring the vanishing of Massey products inintersection cohomology. In the present paper, we study the perverse algebraicmodel of complex projective varieties with isolated singularities. We endowsuch invariant with natural mixed Hodge structures. This allows us to provesome intersection-formality results for large families of complex projectivevarieties, such as isolated surface singularities and varieties of arbitrarydimension with ordinary isolated singularities.

Mixed Hodge structures on the intersection homotopy type of complex varieties with isolated singularities