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

Shin Ichi Matsumura

doi:10.4310/CAG.2014.v22.n4.a1

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

Shin Ichi Matsumura

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	595-616
Number of pages	22
Journal	Communications in Analysis and Geometry
Volume	22
Issue number	4
DOIs	https://doi.org/10.4310/CAG.2014.v22.n4.a1
Publication status	Published - 2014
Externally published	Yes

ASJC Scopus subject areas

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

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10.4310/CAG.2014.v22.n4.a1

Cite this

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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).",

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

Abstract

ASJC Scopus subject areas

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