Rational homotopy of complex projective varieties with normal isolated singularities
Algebraic Topology
2016-03-31 v2 Algebraic Geometry
Abstract
Let X be a complex projective variety of dimension n with only isolated normal singularities. In this paper we prove, using mixed Hodge theory, that if the link of each singular point of X is (n-2)-connected, then X is 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.
Cite
@article{arxiv.1503.05347,
title = {Rational homotopy of complex projective varieties with normal isolated singularities},
author = {David Chataur and Joana Cirici},
journal= {arXiv preprint arXiv:1503.05347},
year = {2016}
}
Comments
Final version to appear in Forum. Math. Exposition improved thanks to the referees comments