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Moduli of algebraic surfaces. (English) Zbl 0658.14017
Theory of moduli, Lect. 3rd Sess. Cent. Int. Mat. Estivo, Montecatini Terme/Italy 1985, Lect. Notes Math. 1337, 1-83 (1988).
[For the entire collection see Zbl 0638.00010.]
The paper is an excellent survey on moduli of algebraic surfaces, mainly directed to and ought to be accessible to non specialists and to beginning graduate students. After a widespread introductory part on deformation theory and an outline on Enriques-Kodaira classification, the paper deals with moduli of surfaces of general type, including an outline of recent work of the author and a result of I. Reider. The main contents is: number of moduli of surfaces of general type, deformation theory of \(({\mathbb{Z}}/2)^ 2\quad covers\) and examples of moduli spaces with arbitrarily many connected components having different dimensions.
Further results are contained in the paper “Everywhere non reduced moduli spaces” (Invent. Math., to appear).
Reviewer: M.Beltrametti

MSC:
14J10 Families, moduli, classification: algebraic theory
14D15 Formal methods and deformations in algebraic geometry