2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150371Let $X$ be a compact complex manifold of dimension $n\ge 2$ 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 $1<r<n-1$.AMS-TeX v2.1, 19 pagesAlgebraic Geometry14J60 (Primary) 14C20, 14F05, 14J40 (Secondary)text