H. Popp

Moduli Theory and Classification Theory of Algebraic Varieties

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Lecture Notes in Mathematics 620
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-08522-5
• 1977.
• Seitenzahl: 196
• Erscheinungstermin: 1. November 1977
• Englisch
• Abmessung: 235mm x 155mm x 11mm
• Gewicht: 323g
• ISBN-13: 9783540085225
• ISBN-10: 354008522X
• Artikelnr.: 23562290

Inhaltsangabe

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.