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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 117–134 (Mi izv1609)  

The influence of height on degenerations of algebraic surfaces of type $K3$

A. N. Rudakov, T. Tsink, I. R. Shafarevich


Abstract: The authors announce the conjecture that a family of $K3$ surfaces the Artin height of whose generic fiber is greater than $2$ does not degenerate; they prove this conjecture for surfaces of degree $2$. As a corollary it is shown that a family of supersingular $K3$ surfaces does not degenerate; i.e., its variety of moduli is complete.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 119–135

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J25; Secondary 14L05
Received: 03.08.1981

Citation: A. N. Rudakov, T. Tsink, I. R. Shafarevich, “The influence of height on degenerations of algebraic surfaces of type $K3$”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 117–134; Math. USSR-Izv., 20:1 (1983), 119–135

Citation in format AMSBIB
\Bibitem{RudTsiSha82}
\by A.~N.~Rudakov, T.~Tsink, I.~R.~Shafarevich
\paper The influence of height on degenerations of algebraic surfaces of type~$K3$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 1
\pages 117--134
\mathnet{http://mi.mathnet.ru/izv1609}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=643897}
\zmath{https://zbmath.org/?q=an:0509.14036|0492.14024}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 119--135
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001343}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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