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Push-forward of degeneracy classes and ampleness

Authors:	Jø rgen Anders Geertsen

Institution:	Department of Mathematics, Sproul Hall, University of California, Riverside, California 92521

Abstract:	Let be a projective variety and vector bundles on . Suppose $g: X \rightarrow Y$ is a surjective map onto another variety . Let $\phi: E \rightarrow F$ be any vector bundle map and $X_{k}(\phi)$ the 'th degeneracy locus of $\phi$ . We show that the dimension of $g(X_{k}(\phi))$ is at least equal to $\begin{displaymath}\min\{ {\dim }Y, { \dim }X - (\text{rank }E-k)(\text{rank }F -k) \}\end{displaymath}$ under the hypothesis that $E^{*} \otimes F$ is an ample vector bundle on .

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