Factors of Jacobians and isotrivial elliptic surfaces

A. Libgober

Journal of Singularities
volume 5 (2012), 115-123
Proceedings of the International Conference on Singularity Theory and Applications, Hefei, China, July 25-31, 2011

Received 26 December 2012. Received in revised form 23 April 2012.

DOI: 10.5427/jsing.2012.5i

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We show that the rank of the Mordell-Weil group of an isotrivial elliptic surface over C(t) can be calculated as the number of isogeny factors which are elliptic curves in the jacobian of the cyclic cover of a projective line associated to the elliptic surface. We illustrate this method by calculating the ranks in several examples, some of which recover already known results, and discuss relation between open questions on factors of jacobians and elliptic surfaces.

Author(s) information:

A. Libgober
Department of Mathematics
University of Illinois
Chicago, IL 60607 U.S.A.
Department of Mathematics
University of Miami
Coral Gables, FL 33146 U.S.A.
email: libgober@math.uic.edu