Slope equalities for genus 5 surface fibrations

Details Slope equalities for genus 5 surface fibrations Slope equalities for genus 5 surface fibrations

2010-06-15

arxiv.org/abs/1006.3036v1

Mathematics

Algebraic Geometry

22 pages, no figures. This incorporates the previous article arXiv:0804.0388v1

Scientific paper

K. Konno proved a slope equality for fibred surfaces with fibres of odd genus and general fibre of maximal gonality. More precisely he found a relation between the invariants of the fibration and certain weights of special fibres (called the Horikawa numbers). We give an alternative and more geometric proof in the case of a genus 5 fibration, under generality assumptions. In our setting we are able to prove that the fibre with positive Horikawa numbers are precisely the trigonal ones, we compute their weights explicitly and thus we exhibit explicit examples of regular surfaces with assigned invariants and Horikawa numbers.

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