Weak Lefschetz theorems and the topology of zero loci of ample vector bundles

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Abstract

The purpose of this paper is to study the fundamental group and higher homotopy groups of the zero locus of holomorphic sections of ample vector bundles on projective varieties, in the spirit of the Lefschetz hyperplane theorem. We give some Lefschetz type theorems by using Morse theory and the method of Napier-Ramachandran (the L2-method and the theory of formal schemes).

Original languageEnglish
Pages (from-to)595-616
Number of pages22
JournalCommunications in Analysis and Geometry
Volume22
Issue number4
DOIs
Publication statusPublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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