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Birationality of \'Etale Morphisms via Surgery by Nollet, Scott; Taylor, Laurence R.; Xavier, Frederico is a scholarly article available to read on EtoBox.

What is Birationality of \'Etale Morphisms via Surgery about?

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover away from $D$ has degree $d=1$ or $d=\infty$ (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 $F:X \to \Bbb C^n$ of algebraic varieties which covers away from such a hypersurface $D$ must be birational.

Author

Nollet, Scott; Taylor, Laurence R.; Xavier, Frederico

Published

2007

Language

EN