Push-forward of degeneracy classes and ampleness
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- by Jørgen Anders Geertsen PDF
- Proc. Amer. Math. Soc. 129 (2001), 1885-1890 Request permission
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 \[ \min \{ {\dim }Y, { \dim }X - (\text {rank }E-k)(\text {rank }F -k) \}\] under the hypothesis that $E^{*} \otimes F$ is an ample vector bundle on $X$.References
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Additional Information
- Jørgen Anders Geertsen
- Affiliation: Department of Mathematics, Sproul Hall, University of California, Riverside, California 92521
- Email: geertsen@math.ucr.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1885-1890
- MSC (2000): Primary 14C17; Secondary 14M12
- DOI: https://doi.org/10.1090/S0002-9939-00-05881-0
- MathSciNet review: 1825909