Moduli Theory and Classification Theory of Algebraic Varieties

1. Auflage 1977
ISBN: 978-3-540-08522-5
Verlag: Springer

Buch, Englisch, Band 620, 189 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 306 g

Reihe: Lecture Notes in Mathematics

Springer Book Archives

Zielgruppe

Research

Autoren/Hrsg.

Popp, H.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.