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Revista Matemática Complutense

, Volume 31, Issue 2, pp 479–524 | Cite as

Rational homotopy and intersection-formality of complex algebraic varieties

  • David Chataur
  • Joana Cirici
Article
  • 62 Downloads

Abstract

A homotopical treatment of intersection cohomology recently developed by Chataur–Saralegui–Tanré 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.

Keywords

Rational homotopy Formality Intersection cohomology Mixed Hodge theory Weight spectral sequence Isolated singularities 

Mathematics Subject Classification

55P62 55N33 32S35 

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Copyright information

© Universidad Complutense de Madrid 2018

Authors and Affiliations

  1. 1.LAMFA Université de Picardie Jules VerneAmiens Cedex 1France
  2. 2.Fachbereich Mathematik und InformatikUniversität MünsterMünsterGermany

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