A new proof of the global Torelli theorem for K3 surfaces. (English) Zbl 0559.14004

The aim of this paper is to give a new proof of the global Torelli theorem for algebraic K3 surfaces. The method of proof consists in interpreting the theorem of Kulikov-Persson-Pinkham [cf. V. S. Kulikov, Math. USSR, Izv. 11, 957-989 (1977); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 41, 1008-1042 (1977; Zbl 0367.14014) and U. Persson and H. Pinkham, Ann. Math., II. Ser. 113, 45-66 (1981; Zbl 0426.14015)] on degenerations of K3 surfaces as a way to construct partial compactifications of the moduli spaces of polarized K3 surfaces. Analogous constructions of partial compactifications of the appropriate period spaces have been given by Mumford. The proof then reduces to a degree calculation, which is done via an analysis of the limiting mixed Hodge structures.


14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14J15 Moduli, classification: analytic theory; relations with modular forms
32J05 Compactification of analytic spaces
14J25 Special surfaces
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
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