Elliptic Fibrations on a Generic Jacobian Kummer Surface
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Kumar_Elliptical fibrations.pdf
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414.33 KB
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Author(s)
Kumar, Abhinav
Date Issued
May 2014
Journal
Journal of Algebraic Geometry
Publisher
American Mathematical Society (AMS)
Citation
Kumar, Abhinav
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://www.ams.org/journals/jag/2014-23-04/S1056-3911-2014-00620-2/
