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arXiv · 0707.2612

Exceptional covers of surfaces

Jeff Achter
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Abstract

Consider a finite morphism f:X -> Y of smooth projective varieties over a finite field k. Suppose X is the vanishing locus in projective N-space of at most r forms of degree at most d. We show there is a constant C, depending only on N, r, d and deg(f) such that if #k > C, then f(k):X(k) -> Y(k) is injective if and only if it's surjective.

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Jeff Achter. 2007-07-18. Exceptional covers of surfaces. https://doi.org/10.4153/cmb-2010-049-7

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