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Push-forward of degeneracy classes and ampleness

Author: Jørgen Anders Geertsen
Journal: Proc. Amer. Math. Soc. 129 (2001), 1885-1890
MSC (2000): Primary 14C17; Secondary 14M12
Published electronically: December 13, 2000
MathSciNet review: 1825909
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Abstract: Let $X$ be a projective variety and $E,F$ vector bundles on $X$. Suppose $g: X \rightarrow Y$ is a surjective map onto another variety $Y$. Let $\phi: E \rightarrow F$ be any vector bundle map and $X_{k}(\phi)$ the $k$'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 $X$.

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Additional Information

Jørgen Anders Geertsen
Affiliation: Department of Mathematics, Sproul Hall, University of California, Riverside, California 92521

Received by editor(s): September 7, 1998
Received by editor(s) in revised form: October 15, 1999
Published electronically: December 13, 2000
Communicated by: Ron Donagi
Article copyright: © Copyright 2000 American Mathematical Society

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