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Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
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Giuseppe Borrelli
Published/Copyright:
August 19, 2009
Abstract
We investigate surfaces of general type S with χ(S) = 1 that admit a fibration ƒ : S → ℙ1 whose general fiber is a hyperelliptic curve of genus 3. We show that the bicanonical map of S factors through a generically finite rational map of degree two onto a ruled surface.
Together with a previous result, this yields a characterization of surfaces with χ = 1 whose bicanonical map factors through a 2 : 1 map onto a ruled surface in terms of the existence of fibrations of small genus.
Received: 2007-10-16
Revised: 2008-08-21
Published Online: 2009-08-19
Published in Print: 2010-January
© de Gruyter 2010
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- Secant dimensions of low-dimensional homogeneous varieties
- Peano differentiable extensions in o-minimal structures
- Global properties of codimension two spacelike submanifolds in Minkowski space
- Local recognition of the line graph of an anisotropic vector space
- Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
- O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
- Positivity in power series rings
- Scrolls over four dimensional varieties
- Nearly flag-transitive affine planes
Articles in the same Issue
- Secant dimensions of low-dimensional homogeneous varieties
- Peano differentiable extensions in o-minimal structures
- Global properties of codimension two spacelike submanifolds in Minkowski space
- Local recognition of the line graph of an anisotropic vector space
- Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
- O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
- Positivity in power series rings
- Scrolls over four dimensional varieties
- Nearly flag-transitive affine planes
