Brill-Noether theory of binary curves

The theorems of Riemann, Clifford and Martens are proved for every line bundle parametrized by the compactified Jacobian of every binary curve. The Clifford index is used to characterize hyperelliptic and trigonal binary curves. The Brill-Noether theorem for $r\leq 2$ is proved for a general binary curve.

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Published 1 January 2010