This article is cited in 6 papers

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.

UDC: 513.6

MSC: Primary 14J25; Secondary 14L05

Received: 03.08.1981

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

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