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Distinguishing Brill--Noether loci

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Richard Haburcak
Thu, 20/06/2024 - 10:30 - 12:00
MPIM Lecture Hall

Classical BrillNoether theory studies linear systems on a general curve in the moduli space $\mathcal{M}_g$ of algebraic curves of genus $g$. A refined BrillNoether theory studies the linear systems on curves with a given BrillNoether special linear system. As a first step, one would like to understand the stratification of $\mathcal{M}_g$ by BrillNoether loci, which parameterize curves with a particular projective embedding. In this talk, we discuss recent progress on techniques to distinguish BrillNoether loci and we'll introduce new methods using K3 surfaces, resolving a conjecture identifying the maximal loci of the stratification. This is based on joint work with Asher Auel, Andrei Bud, Andreas Leopold Knutsen, and Hannah Larson.

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