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Birationality of étale maps via surgery
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Scott Nollet
Published/Copyright:
January 8, 2009
Abstract
We use a counting argument and surgery theory to show that if D is a sufficiently general algebraic hypersurface in 
, then any local diffeomorphism F : X → of simply connected manifolds which is a d-sheeted cover away from D has degree d = 1 or d = ∞ (however all degrees d > 1 are possible if F fails to be a local diffeomorphism at even a single point). In particular, any étale morphism F : X → of algebraic varieties which covers away from such a hypersurface D must be birational.
Received: 2007-04-26
Revised: 2007-10-07
Published Online: 2009-01-08
Published in Print: 2009-February
© Walter de Gruyter Berlin · New York 2009
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- Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space
- On the growth of nonuniform lattices in pinched negatively curved manifolds
- Extended Picard complexes and linear algebraic groups
- Birationality of étale maps via surgery
- Heights and metrics with logarithmic singularities
- Fredholm realizations of elliptic symbols on manifolds with boundary
- Correspondences with split polynomial equations
- A parabolic free boundary problem with Bernoulli type condition on the free boundary
Articles in the same Issue
- Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space
- On the growth of nonuniform lattices in pinched negatively curved manifolds
- Extended Picard complexes and linear algebraic groups
- Birationality of étale maps via surgery
- Heights and metrics with logarithmic singularities
- Fredholm realizations of elliptic symbols on manifolds with boundary
- Correspondences with split polynomial equations
- A parabolic free boundary problem with Bernoulli type condition on the free boundary
