We describe a conjectural stratification of the Brill- Noether variety for general curves of fixed genus and gonality. As evidence for this conjecture, we show that this Brill-Noether variety has at least as many irreducible components as predicted by the conjecture and that each of these components has the expected dimension. Our proof uses combinatorial and tropical techniques. Specifically, we analyze containment relations between the various strata of tropical Brill-Noether loci identified by Pflueger in his classification of special divisors on chains of loops.
|Number of pages
|Michigan Mathematical Journal
|Published - Mar 2022
Bibliographical noteFunding Information:
Received July 22, 2019. Revision received October 13, 2019. The second author was supported by NSF DMS-1601896.
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ASJC Scopus subject areas
- Mathematics (all)