Details

Autor(en) / Beteiligte

• Popp, Herbert

Titel

Moduli Theory and Classification Theory of Algebraic Varieties

Ist Teil von

• Lecture Notes in Mathematics : 620

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1977

Beschreibungen/Notizen

• 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