Syzygies of secant varieties of smooth projective curves and gonality sequences

Junho Choe; Sijong Kwak; Jinhyung Park

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arXiv · 2307.03405

Syzygies of secant varieties of smooth projective curves and gonality sequences

Junho Choe·Sijong Kwak·Jinhyung Park

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Abstract

The purpose of this paper is to prove that one can read off the gonality sequence of a smooth projective curve from syzygies of secant varieties of the curve embedded by a line bundle of sufficiently large degree. More precisely, together with Ein-Niu-Park's theorem, our main result shows that the gonality sequence of a smooth projective curve completely determines the shape of the minimal free resolutions of secant varieties of the curve of sufficiently large degree. This is a natural generalization of the gonality conjecture on syzygies of smooth projective curves established by Ein-Lazarsfeld and Rathmann to the secant varieties.

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Junho Choe, Sijong Kwak, Jinhyung Park. 2023-07-07. Syzygies of secant varieties of smooth projective curves and gonality sequences. https://arxiv.org/abs/2307.03405

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