Our findings demonstrate non-containment of projectivized strata of differentials in Brill-Noether divisors, suggesting implications for quadratic differentials.
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 M g M_g . Our results regarding quadratic differentials imply that the quadratic strata in genus 6 6 are uniruled.
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Andrei Bud (2025) studied this question.
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