Moduli theory and classification theory of algebraic varieties (Lecture notes in mathematics ; 620)

Popp, Herbert

ISBN 10: 038708522X ISBN 13: 9780387085227

Publisher: Springer-Verlag, 1977

Synopsis

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.

Edition details

• Publisher: Springer-Verlag
• Publication date: 1977
• Language: English
• ISBN 10: 038708522X
• ISBN 13: 9780387085227
• Binding: Unknown Binding
• Number of pages: 189