Elliptic fibrations on a generic Jacobian Kummer surface

Kumar, Abhinav

doi:10.1090/S1056-3911-2014-00620-2

Author: Abhinav Kumar
Journal: J. Algebraic Geom. 23 (2014), 599-667
DOI: https://doi.org/10.1090/S1056-3911-2014-00620-2
Published electronically: May 28, 2014
MathSciNet review: 3263663
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Abstract | References | Additional Information

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.

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Additional Information

Abhinav Kumar
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 694441
Email: abhinav@math.mit.edu

Received by editor(s): April 20, 2011
Received by editor(s) in revised form: February 15, 2012
Published electronically: May 28, 2014
Additional Notes: The author was supported in part by NSF grants DMS-0757765 and DMS-0952486, and by a grant from the Solomon Buchsbaum Research Fund. He thanks Princeton University for its hospitality during the period when this project was started.
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