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The gonality of complete intersection curves (1706.08169v7)
Published 25 Jun 2017 in math.AG
Abstract: The purpose of this paper is to show that for a complete intersection curve $C$ in projective space (other than a few stated exceptions), any morphism $f: C \to \mathbb{P}r$ satisfying $\text{deg}\, f*\mathcal{O}_{\mathbb{P}r}(1) <\text{deg}\, C$ is obtained by projection from a linear space. In particular, we obtain bounds on the gonality of such curves and compute the gonality of general complete intersection curves. We also prove a special case of one of the well-known Cayley-Bacharach conjectures posed by Eisenbud, Green, and Harris.