Elliptic fibrations on a generic Jacobian Kummer surface

Details Elliptic fibrations on a generic Jacobian Kummer surface Elliptic fibrations on a generic Jacobian Kummer surface

2011-05-09

arxiv.org/abs/1105.1715v1

Mathematics

Algebraic Geometry

45 pages, 5 figures

Scientific paper

We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic zero, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the twenty five different fibrations, and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question of Kuwata and Shioda.

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