nLab David Mumford

Selected writings

David Mumford is an algebraic geometer, who sharply switched at some point in his career to study pattern recognition. His contributions include the creation of modern geometric invariant theory (as a method of building moduli spaces), the introduction of Deligne-Mumford stacks and especially of the Deligne-Mumford compactification of the moduli space of curves, the Mumford-Tate curve, Mumford cohomological classes on the moduli space of curves, Mumford conjecture (recently proved by Madsen and Weiss), the classification of algebraic surfaces in positive characteristics and solutions to a number of difficult problems in mainstream algebraic geometry. He is also well known for clear exposition, and wrote several books on algebraic geometry (Tata lectures on theta, Geometric invariant theory, “Red book”…).

Scans of most, if not all, his papers are available at his

Selected writings

On geometric invariant theory:

Introducing the notion of algebraic stacks and (what came to be called) Deligne-Mumford stacks, and on the example of the moduli space of curves:

category: people

Last revised on April 16, 2023 at 13:38:04. See the history of this page for a list of all contributions to it.