Let be a field and let be a smooth projective curve defined over the field and has genus . The function field of will be denoted by . An elliptic surface over the curve is, by definition, a two-dimensional projective variety together with:
The surface is an elliptic surface over the curve . It may be regarded as an elliptic curve over the function field .
- 1 R. Miranda, The basic theory of elliptic surfaces, Dottorato di Ricerca in Matematica, Dipartimento di Mathematica dell’ UniversitÃÂ di Pisa, ETS Editrice Pisa, 1989.
- 2 J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 151, Springer-Verlag, New York.
|Date of creation||2013-03-22 15:34:16|
|Last modified on||2013-03-22 15:34:16|
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