Elliptic Fibrations on a Generic Jacobian Kummer Surface
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 compu...
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| Format: | Article |
| Language: | English |
| Published: |
American Mathematical Society (AMS),
2015-01-22T16:24:49Z.
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| Online Access: | Get fulltext |
| Summary: | 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. National Science Foundation (U.S.) (Grant DMS-0757765) National Science Foundation (U.S.) (Grant DMS-0952486) Solomon Buchsbaum AT&T Research Fund |
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