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arXiv · 1706.08169

The gonality of complete intersection curves

James Hotchkiss·Chung Ching Lau·Brooke Ullery
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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.

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James Hotchkiss, Chung Ching Lau, Brooke Ullery. 2017-06-25. The gonality of complete intersection curves. https://arxiv.org/abs/1706.08169

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