2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150372A new genus $g=g(X,\ce)$ is defined for the pairs $(X,\ce)$ that consist of $n$-dimensional compact complex manifolds $X$ and ample vector bundles $\ce$ of rank $r$ less than $n$ on $X$. In case $r=n-1$, $g$ is equal to curve genus. Above pairs $(X,\ce)$ with $g$ less than two are classified. For spanned $\ce$ it is shown that $g$ is greater than or equal to the irregularity of $X$, and its equality condition is given.AMS-TeX v2.1, 8 pagesAlgebraic Geometry14J60 (Primary) 14C20, 14F05, 14J40 (Secondary)text