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Exceptional Covers of Surfaces

Published online by Cambridge University Press:  20 November 2018

Jeffrey D. Achter
Jeffrey D. Achter*
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523 e-mail: [email protected]
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Abstract

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Consider a finite morphism $f\,:\,X\,\to \,Y$ of smooth, projective varieties over a finite field $\mathbb{F}$. Suppose $X$ is the vanishing locus in ${{\mathbb{P}}^{N}}$ of $r$ forms of degree at most $d$. We show that there is a constant $C$ depending only on $(N,\,r,\,d)$ and $\deg (f)$ such that if $\left| \mathbb{F} \right|\,>\,C$, then $f\,(\mathbb{F})\,:\,X(\mathbb{F})\,\to Y(\mathbb{F})$ is injective if and only if it is surjective.

Keywords

11G25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 385 - 393
Copyright
Copyright © Canadian Mathematical Society 2010

References

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