Surveys in Differential Geometry

Volume 14 (2009)

Brill-Noether theory

Pages: 131 – 144



Joe Harris


In this paper I’ll try to give an overview of one of the central threads in the study of algebraic curves: Brill-Noether theory. After an initial discussion in Section 1 of what I mean by Brill-Noether theory, and a discussion of the role it plays in our understanding of algebraic curves, I’ll give in Section 2 a summary of what is known. Finally, Sections 3 and 4 represent the real point of the paper: in these, I’ll give two possible answers to the question, “where do we go from here?”

Published 1 January 2009