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