Moduli Theory and Classification Theory of Algebraic Varieties

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