Rational homotopy of complex projective varieties with normal isolated\n singularities

2015/03/18 by David Chataur, Chataur, David, Joana Cirici +1
Mathematics · Physics and Astronomy · #32S35 #55P62 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1503.05347

openalex publication_date 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a complex projective variety of dimension n with only isolated\nnormal singularities. In this paper we prove, using mixed Hodge theory, that if\nthe link of each singular point of X is (n-2)-connected, then X is a formal\ntopological space. This result applies to a large class of examples, such as\nnormal surface singularities, varieties with ordinary multiple points,\nhypersurfaces with isolated singularities and more generally, complete\nintersections with isolated singularities. We obtain analogous results for\ncontractions of subvarieties.\n

Related

• Mixed Hodge Structures on the rational homotopy type of intersection spaces
• Mixed Hodge structures on the intersection homotopy type of complex\n varieties with isolated singularities
• The maximum number of singular points on rational homology projective planes
• Families of singular algebraic varieties that are rationally elliptic spaces
• Hodge symmetry and Lefschetz theorems for singular varieties