Exceptional Covers of Surfaces

Canadian mathematical bulletin

Jeffrey D. Achter¹ 

[1] Department of Mathematics, Colorado State University, Fort Collins, CO, USA

关键词: graph;    $(g;    f)$-factor;    $(g;    f;    n)$-critical graph;    binding number;   

DOI  :  10.4153/CMB-2010-049-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Consider a finite morphism $f: X ightarrow Y$ of smooth, projective varieties over a finite field $mathbf{F}$. Suppose $X$ is the vanishing locus in $mathbf{P}^N$ 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 $|{mathbf{F}}|>C$, then $f(mathbf{F}): X(mathbf{F}) ightarrow Y(mathbf{F})$ is injective if and only if it is surjective.

【 授权许可】

Unknown