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arXiv · alg-geom/9709023

A generalization of curve genus for ample vector bundles, II

Yoshiaki Fukuma·Hironobu Ishihara
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Abstract

Let $X$ 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 $1<r<n-1$.

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Yoshiaki Fukuma, Hironobu Ishihara. 1997-09-22. A generalization of curve genus for ample vector bundles, II. https://arxiv.org/abs/alg-geom/9709023

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