Surveys in Differential Geometry

Volume 14 (2009)

Brill-Noether theory

Pages: 131 – 144

DOI: http://dx.doi.org/10.4310/SDG.2009.v14.n1.a5

Author

Joe Harris

Abstract

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?”

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