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arXiv · 1209.6278

Notes on hyperelliptic fibrations of genus 3, I

Masaaki Murakami
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Abstract

We shall study the structure of hyperelliptic fibrations of genus 3, from the view point given by Catanese and Pignatelli in arXiv:math/0503294. In this part I, we shall give a structure theorem for such fibrations for the case of f : S \to B with all fibers 2-connected. We shall also give, for the case of B projective line, sufficient conditions for the existence of such fibrations from the view point of our structure theorem, prove the uniqueness of the deformation type and the simply connectedness of S for some cases, and give some examples including those with minimal regular S with geometric genus 4 and the first Chern number 8. The last example turns out to be a member of the family M_0 given in Bauer--Pignatelli arXiv:math/0603094.

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Masaaki Murakami. 2012-09-27. Notes on hyperelliptic fibrations of genus 3, I. https://arxiv.org/abs/1209.6278

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