Geometric invariant theory. 2nd enlarged ed. (English) Zbl 0504.14008

Mumford, D.; Fogarty, J.

Ergebnisse der Mathematik und ihrer Grenzgebiete. 34. Berlin-Heidelberg-New York: Springer-Verlag. XII, 220 p. DM 74.00; $ 32.90 (1982).

MSC:

14L24	Geometric invariant theory
14D20	Algebraic moduli problems, moduli of vector bundles
14-02	Research exposition (monographs, survey articles) pertaining to algebraic geometry
14K10	Algebraic moduli of abelian varieties, classification
14C05	Parametrization (Chow and Hilbert schemes)
14D22	Fine and coarse moduli spaces
14H55	Riemann surfaces; Weierstrass points; gap sequences
14H10	Families, moduli of curves (algebraic)
14H40	Jacobians, Prym varieties
20G15	Linear algebraic groups over arbitrary fields
14K25	Theta functions and abelian varieties
14L30	Group actions on varieties or schemes (quotients)

Keywords:

geometrically reductive linear algebraic group; finite generation of ring of invariants; stability of Chow form; polynomial ring of invariants; moduli problems; algebraic space; K3 surfaces; moduli of vector bundles; theoretical physics; compactifications of moduli spaces; theta functions; Schottky problem; Torelli theorem; higher Weierstrass points

Citations:

Zbl 0147.393; Zbl 0316.14016; Zbl 0406.14031; Zbl 0286.14014; Zbl 0289.14010; Zbl 0409.13004; Zbl 0363.14003; Zbl 0375.14013; Zbl 0359.14005; Zbl 0219.14024; Zbl 0372.35002; Zbl 0299.14014; Zbl 0316.14010; Zbl 0346.35025; Zbl 0386.35002; Zbl 0326.35011; Zbl 0366.10023; Zbl 0402.10028