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Elliptic fibrations on a generic Jacobian Kummer surface

By Abhinav Kumar

Abstract

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 0, 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 25 different fibrations and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008.Comment: 47 pages, 5 figures. Final versio

Topics: Mathematics - Algebraic Geometry, 14J27, 14J28, 14H45
Year: 2014
DOI identifier: 10.1090/S1056-3911-2014-00620-2
OAI identifier: oai:arXiv.org:1105.1715
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