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Forum Mathematicum

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Volume 29, Issue 1


Rational homotopy of complex projective varieties with normal isolated singularities

David Chataur
  • Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne 33, rue Saint-Leu, 80039 Amiens Cedex 1, France
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/ Joana Cirici
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  • Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany
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Published Online: 2016-06-18 | DOI: https://doi.org/10.1515/forum-2015-0101


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.

Keywords: Rational homotopy; mixed Hodge theory; weight filtration; fundamental groups; formality,singular varieties; isolated singularities; contractions

MSC 2010: 55P62; 32S35


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About the article

Received: 2015-05-27

Revised: 2016-01-07

Published Online: 2016-06-18

Published in Print: 2017-01-01

Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: SPP-1786

Funding Source: Ministerio de Economía y Competitividad

Award identifier / Grant number: MTM2013-42178-P

The second-named author would like to acknowledge financial support from the German Research Foundation through project SPP-1786 and partial support from the Spanish Ministry of Economy and Competitiveness through project MTM2013-42178-P.

Citation Information: Forum Mathematicum, Volume 29, Issue 1, Pages 41–57, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0101.

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David Chataur and Joana Cirici
Revista Matemática Complutense, 2018

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