Rational homotopy of complex projective varieties with normal isolated singularities

AbstractLetXbe a complex projective variety of dimensionnwith only isolated normal singularities. In this paper, we prove, using mixed Hodge theory, that if the link of each singular point ofXis(n-2)${(n-2)}$-connected, thenXis a formal topological space. This result applies to a large class of examples, such as normal surface singularities, varieties with ordinary multiple points, hypersurfaces with isolated singularities and, more generally, complete intersections with isolated singularities. We obtain analogous results for contractions of subvarieties.