Birationality of etale maps via surgery

被引：7

作者：

Nollet, Scott ^{[1
]}

Taylor, Laurence R. ^{[2
]}

Xavier, Frederico ^{[2
]}

机构：

[1] Texas Christian Univ, Dept Math, Ft Worth, TX 76129 USA

[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2009年 / 627卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1515/CRELLE.2009.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use a counting argument and surgery theory to show that if D is a sufficiently general algebraic hypersurface in C-n, then any local diffeomorphism F : X -> C-n of simply connected manifolds which is a d-sheeted cover away from D has degree d - 1 or d - infinity (however all degrees d > 1 are possible if F fails to be a local diffeomorphism at even a single point). In particular, any etale morphism F : X -> C-n of algebraic varieties which covers away from such a hypersurface D must be birational.

引用

页码：83 / 95

页数：13

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