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arXiv · 2402.11599

Brill-Noether loci and strata of differentials

Andrei Bud
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Abstract

We prove that the projectivized strata of differentials are not contained in pointed Brill-Noether divisors, with only a few exceptions. For a generic element in a stratum of differentials, we show that many of the associated pointed Brill-Noether loci are of expected dimension. We use our results to study the Auel-Haburcak Conjecture: We obtain new non-containments between maximal Brill-Noether loci in $\mathcal{M}_g$. Our results regarding quadratic differentials imply that the quadratic strata in genus $6$ are uniruled.

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Andrei Bud. 2024-02-18. Brill-Noether loci and strata of differentials. https://arxiv.org/abs/2402.11599

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