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Bicanonical map of surfaces with १ = 1 fibered by hyperelliptic curves of genus 3

Bicanonical map of surfaces with १ = 1 fibered by hyperelliptic curves of genus 3 We investigate surfaces of general type S with १( S ) = 1 that admit a fibration ƒ : S → ℙ 1 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 १ = 1 whose bicanonical map factors through a 2 : 1 map onto a ruled surface in terms of the existence of fibrations of small genus. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Bicanonical map of surfaces with १ = 1 fibered by hyperelliptic curves of genus 3

Borrelli, Giuseppe
Advances in Geometry , Volume 10 (1) – Jan 1, 2010
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17 pages

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Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1615-715X
eISSN
1615-7168
DOI
10.1515/ADVGEOM.2009.035
Publisher site
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Abstract

We investigate surfaces of general type S with १( S ) = 1 that admit a fibration ƒ : S → ℙ 1 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 १ = 1 whose bicanonical map factors through a 2 : 1 map onto a ruled surface in terms of the existence of fibrations of small genus.

Journal

Advances in Geometry – de Gruyter

Published: Jan 1, 2010

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