Elliptic fibrations on a generic Jacobian Kummer surface

We describe all the elliptic fibrations with section on the Kummer surface X X of the Jacobian of a very general curve C C of genus 2 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X X and the symmetric group on the Weierstrass points of C C . In particula...

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Bibliographic Details
Published in:Journal of algebraic geometry 2014-10, Vol.23 (4), p.599-667
Main Author: Kumar, Abhinav
Format: Article
Language:English
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Summary:We describe all the elliptic fibrations with section on the Kummer surface X X of the Jacobian of a very general curve C C of genus 2 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X X and the symmetric group on the Weierstrass points of C C . In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the reducible fibers and Mordell–Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008.
ISSN:1056-3911
1534-7486
DOI:10.1090/S1056-3911-2014-00620-2