A generalization of curve genus for ample vector bundles, II

Yoshiaki Fukuma and Hironobu Ishihara

Vol. 193 (2000), No. 2, 307–326

DOI: 10.2140/pjm.2000.193.307

Abstract

Let X be a compact complex manifold of dimension n ≥ 2 and ℰ an ample vector bundle of rank r < n on X. As the continuation of Part I, we further study the properties of g(X,ℰ) that is an invariant for pairs (X,ℰ) and is equal to curve genus when r = n − 1. Main results are the classifications of (X,ℰ) with g(X,ℰ) = 2 (resp. 3) when ℰ has a regular section (resp. ℰ is ample and spanned) and 1 < r < n − 1.

Milestones

Received: 5 August 1998

Published: 1 April 2000