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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 5, Pages 213–223 (Mi izv92)  

This article is cited in 3 scientific papers (total in 3 papers)

Some families of Abelian surfaces

I. R. Shafarevich

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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.

DOI: https://doi.org/10.4213/im92

Full text: PDF file (981 kB)
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English version:
Izvestiya: Mathematics, 1996, 60:5, 1083–1093

Bibliographic databases:

MSC: Primary 11G10, 14K15; Secondary 11R52, 14J28
Received: 11.01.1996

Citation: I. R. Shafarevich, “Some families of Abelian surfaces”, Izv. RAN. Ser. Mat., 60:5 (1996), 213–223; Izv. Math., 60:5 (1996), 1083–1093

Citation in format AMSBIB
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\paper Some families of Abelian surfaces
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\yr 1996
\vol 60
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\pages 213--223
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\yr 1996
\vol 60
\issue 5
\pages 1083--1093
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. R. Shafarevich, “Families of reducible algebraic varieties”, Math. Notes, 60:6 (1996), 717–720  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Sun X.T., Tan S.L., Zuo K., “Families of K3 surfaces over curves reaching the Arakelov-Yau type upper bounds and modularity”, Mathematical Research Letters, 10:2–3 (2003), 323–342  crossref  mathscinet  zmath  isi
    3. Viehweg E., Kang Z., “A characterization of certain Shimura curves in the moduli stack of abelian varieties”, Journal of Differential Geometry, 66:2 (2004), 233–287  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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