Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Elliptic fibrations on a generic Jacobian Kummer surface


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
Email: abhinav@math.mit.edu

DOI: https://doi.org/10.1090/S1056-3911-2014-00620-2
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.
Article copyright: © Copyright 2014

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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