Geodesic
Exceptional Covers of Surfaces
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 385-393

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DOI

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.
DOI : 10.4153/CMB-2010-049-7
Mots-clés : 11G25 
Achter, Jeffrey D. Exceptional Covers of Surfaces. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 385-393. doi: 10.4153/CMB-2010-049-7
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     author = {Achter, Jeffrey D.},
     title = {Exceptional {Covers} of {Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {385--393},
     year = {2010},
     volume = {53},
     number = {3},
     doi = {10.4153/CMB-2010-049-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-049-7/}
}
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