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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
##### Keywords:
moduli of algebraic surfaces; deformation theory