Moduli Theory and Classification Theory of Algebraic Varieties

von H. Popp

196 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Algebra
• ISBN: 9783540085225
• Sprache: Englisch
• Erscheinungsdatum: 01.11.1977
• Größe: 235 x 155 mm
• Verlag: Springer