%0 Journal Article
%T A generalization of curve genus for ample vector bundles, I
%A Hironobu Ishihara
%J Mathematics
%D 1997
%I arXiv
%X A 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.
%U http://arxiv.org/abs/alg-geom/9709024v1