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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 5, Pages 1008–1042 (Mi izv1877)  

This article is cited in 54 scientific papers (total in 54 papers)

Degenerations of $K3$ surfaces and Enriques surfaces

Vik. S. Kulikov


Abstract: In this paper we study good (semistable) degenerations of $K3$ surfaces ($m=1$) and Enriques surfaces ($m=2$). We obtain a classification of such degenerations under the condition that the $m$-canonical class is trivial. We show that for each good degeneration there exists a modification satisfying this condition.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:5, 957–989

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J10, 14J15, 14J25; Secondary 14E05, 14E35, 32G30, 32J15
Received: 14.02.1977

Citation: Vik. S. Kulikov, “Degenerations of $K3$ surfaces and Enriques surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 41:5 (1977), 1008–1042; Math. USSR-Izv., 11:5 (1977), 957–989

Citation in format AMSBIB
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\by Vik.~S.~Kulikov
\paper Degenerations of $K3$ surfaces and Enriques surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 5
\pages 1008--1042
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\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 5
\pages 957--989
\crossref{https://doi.org/10.1070/IM1977v011n05ABEH001753}
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    This publication is cited in the following articles:
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    5. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Math. USSR-Izv., 18:2 (1982), 349–380  mathnet  crossref  mathscinet  zmath
    6. A. N. Rudakov, T. Tsink, I. R. Shafarevich, “The influence of height on degenerations of algebraic surfaces of type $K3$”, Math. USSR-Izv., 20:1 (1983), 119–135  mathnet  crossref  mathscinet  zmath
    7. Vik. S. Kulikov, “Decomposition of a birational map of three-dimensional varieties outside codimension 2”, Math. USSR-Izv., 21:1 (1983), 187–200  mathnet  crossref  mathscinet  zmath
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    20. Kondo S., “A Complex Hyperbolic Structure for the Moduli Space of Curves of Genus Three”, J. Reine Angew. Math., 525 (2000), 219–232  mathscinet  zmath  isi
    21. I. Yu. Fedorov, “Divisorial contractions to 3-dimensional $cDV$ points”, Sb. Math., 193:7 (2002), 1091–1102  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    31. V. V. Nikulin, “On the connected components of moduli of real polarized K3-surfaces”, Izv. Math., 72:1 (2008), 91–111  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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