Brill-Noether Generality of Binary Curves

Abstract

We show that the space of linear series of certain multi-degree (including the balanced ones) and rank $r$ on a general binary curve has the expected dimension if nonempty. This generalizes Theorem 24 of Caporaso's paper about binary curves from the case $r\le 2$ to arbitrary rank, and shows that the space of Osserman-limit linear series on a general binary curve has the expected dimension, which was known for $r\le 2$. In addition, we show that this space of linear series is still of expected dimension after imposing certain ramification conditions with respect to a sequence of increasing effective divisors supported on two general points lying on different components of the curve.

Minor changes, to appear in Canadian Mathematical Bulletin

References in corpus (1)

• Lifting divisors on a generic chain of loops