Geodesic
The influence of height on degenerations of algebraic surfaces of type~$K3$
Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 119-135.

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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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A. N. Rudakov; T. Tsink; I. R. Shafarevich. The influence of height on degenerations of algebraic surfaces of type~$K3$. Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 119-135. http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a7/

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