2004, 795 p., Hardcover
ISBN: 0-387-21092-X
About this bookThese 30 articles span the years from 1961-1980 while David Mumford was an active researcher in the area of algebraic geometry. In addition, each of the three sections is introduced with never before published commentary by David Gieseker, Eckart Viehweg, and George Kempf and Herbert Lange.
Table of contents
Part I. Geometric Invariant Theory and the Moduli of Curves * Commentary by David Gieseker * An elementary theorem in geometric invariant theory (1961) * Projective invariants of projective structures and applications (1962) * Periods of a moduli space of bundles on curves (with P. Newstead) (1968) * The structure of the moduli spaces of curves and abelian varieties (1970) * An analytic construction of degenerating curves over complete local rings (1972) * Pathologies IV (1975) * Stability of projective varieties (1977) * On the Kodaira dimension of the moduli space of curves (with J. Harris) (1982) * Towards an enumerative geometry of the moduli space of curves (1983) * Part II. Theta Functions and the Moduli of Abelian Varieties * Commentary by George Kempf and Herbert Lange * On the equations defining abelian varieties. I (1966)* On the equations defining abelian varieties. II (1967) * On the equations defining abelian varieties. III (1967) * Families of abelian varieties (1966) * A note on Shimura’s paper "Discontinuous groups and abelian varieties" (1969) * Theta characteristics of an algebraic curve (1971) * An analytic construction of degenerating abelian varieties over complete rings (1972) * A rank 2 vector bundle of P^4 with 15,000 symmetries (with G. Horrocks) (1973) * Prym Varieties I (1974) * A new approach to compactifying locally symmetric varieties (1973) * Hirzebruch’s Proportionality Theorem in the Non-Compact Case (1977) * On the Kodaira dimension of the Siegel modular variety (1983) * Part III. The Classification of Surfaces and Other Varieties * Commentary by Eckart Viehweg * Enriques’ classification of surfaces in char p: I (1969) * Enriques’ classification of surfaces in char p: II (with E. Bombieri) (1979) * Enriques’ classification of surfaces in char p: III (with E. Bombieri) (1976) * Pathologies of modular algebraic surfaces (1961) * Further pathologies in algebraic geometry (1962) * Pathologies III (1967) * Rational equivalence of 0-cycles on surfaces (1969) * Some elementary examples of unirational varieties which are not rational (with M. Artin) (1972) * An algebraic surface with K ample, (K^2) = 9, p_g = q = 0 (1979)