Selected Papers

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 algebraicsurfaces (1961) Further pathologies in algebraic geometry (1962) Pathologies III (1967) Rational equivalence of 0-cycles on surfaces (1969) Some elementary examples of unirational

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.
Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.