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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Rudakov et al. (1983) studied this question.