Moduli Theory and Classification Theory of Algebraic Varieties

Herbert Popp (auth.)354008522X, 9783540085225, 038708522X

Table of contents :
Moduli theory of algebraic varieties and classification theory of compact complex spaces….Pages 1-17
Moduli spaces for polarized algebraic varieties….Pages 18-31
Group quotients in the category of analytic spaces and the category of algebraic spaces….Pages 32-43
Applications of the quotient theorems to moduli of algebraic varieties….Pages 44-54
Quotients for affine schemes by reductive algebraic groups….Pages 55-67
Quotients in the category of schemes….Pages 68-78
Mumford’s construction of the moduli variety for curves and polarized abelian varieties. Other applications of Mumford’s quotient theory….Pages 79-92
Other methods of treating moduli problems. Artin’s method of algebraic stacks. Griffiths’s method of period maps….Pages 93-116
Compactification of moduli spaces….Pages 117-128
Fine moduli spaces. The universal families for stable curves with level n-structure….Pages 129-143
Applications of moduli theory to fibre spaces and the additivity formula for the Kodaira dimension of fibre spaces. Open problems….Pages 144-158