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arXiv · 2206.04610

Maximal Brill-Noether loci via K3 surfaces

Asher Auel·Richard Haburcak
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Abstract

We explain a strategy for distinguishing Brill-Noether loci in the moduli space of curves by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill-Noether loci with respect to containment. Via an analysis of the stability of Lazarsfeld-Mukai bundles, we obtain new lifting results for linear systems of rank 3 which suffice to prove the maximal Brill-Noether loci conjecture in genus 9-19, 22, and 23.

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Asher Auel, Richard Haburcak. 2022-06-09. Maximal Brill-Noether loci via K3 surfaces. https://arxiv.org/abs/2206.04610

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