Moduli theory and classification theory of algebraic varieties

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Bibliographic Information

Moduli theory and classification theory of algebraic varieties

Herbert Popp

(Lecture notes in mathematics, 620)

Springer-Verlag, 1977

  • : Berlin
  • : New York

Other Title

Moduli theory and classification theory

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Note

Bibliography: p. 178-185

Includes index

Description and Table of Contents

Table of Contents

Moduli theory of algebraic varieties and classification theory of compact complex spaces.- Moduli spaces for polarized algebraic varieties.- Group quotients in the category of analytic spaces and the category of algebraic spaces.- Applications of the quotient theorems to moduli of algebraic varieties.- Quotients for affine schemes by reductive algebraic groups.- Quotients in the category of schemes.- Mumford's construction of the moduli variety for curves and polarized abelian varieties. Other applications of Mumford's quotient theory.- Other methods of treating moduli problems. Artin's method of algebraic stacks. Griffiths's method of period maps.- Compactification of moduli spaces.- Fine moduli spaces. The universal families for stable curves with level n-structure.- Applications of moduli theory to fibre spaces and the additivity formula for the Kodaira dimension of fibre spaces. Open problems.

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