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Projectivity of complete moduli. (English) Zbl 0684.14002
The paper develops a method to establish the projectivity of certain moduli spaces. The general framework uses some results of E. Viehweg [“Weak positivity and the stability of certain Hilbert points”, Invent. Math. 96, No.3, 639-667 (1989)] but develops in a different direction. The general criteria are applied to show the projectivity of the moduli of stable curves in every characteristic. Partial results are obtained for the moduli of surfaces. The compactification of the Picard schemes constructed by A. B. Altman and S. L. Kleiman [Adv. Math. 35, 50-112 (1980), and Am. J. Math. 101, 10-41 (1979; Zbl 0427.14015 and 14016)] is also shown to be projective.
Reviewer: J.Kollár

MSC:
14D20 Algebraic moduli problems, moduli of vector bundles
14J10 Families, moduli, classification: algebraic theory
14H10 Families, moduli of curves (algebraic)
14N05 Projective techniques in algebraic geometry
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