Some families of Abelian surfaces
Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 1083-1093
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It is proved that for all algebraic curves $\Gamma$ that are coverings of given degree $n$ of a given curve $\Gamma_0$ and all non-constant families of “false elliptic curves” over $\Gamma$, their generic fibres belong to only finitely many types up to isomorphism over the algebraic closure of the field of rational functions on $\Gamma$. Applications to the theory of K3 surfaces are mentioned.
@article{IM2_1996_60_5_a9,
author = {I. R. Shafarevich},
title = {Some families of {Abelian} surfaces},
journal = {Izvestiya. Mathematics },
pages = {1083--1093},
publisher = {mathdoc},
volume = {60},
number = {5},
year = {1996},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a9/}
}
I. R. Shafarevich. Some families of Abelian surfaces. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 1083-1093. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a9/