Communications in Analysis and Geometry

Volume 22 (2014)

Number 4

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

Pages: 595 – 616



Shin-Ichi Matsumura (Department of Mathematics and Computer Sciences, Kagoshima University, Kagoshima, Japan)


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 $L^2$-method and the theory of formal schemes).

Full Text (PDF format)