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Prym-Brill-Noether loci of special curves

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Author(s)

Steven Creech, Yoav Len, Caelan Ritter, Derek Wu

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Abstract

We use Young tableaux to compute the dimension of Vr⁠, the Prym–Brill–Noether locus of a folded chain of loops of any gonality. This tropical result yields a new upper bound on the dimensions of algebraic Prym–Brill–Noether loci. Moreover, we prove that Vr is pure dimensional and connected in codimension 1 when dimVr≥1⁠. We then compute the 1st Betti number of this locus for even gonality when the dimension is exactly 1 and compute the cardinality when the locus is finite and the edge lengths are generic.
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Original languageEnglish
Number of pages41
JournalInternational Mathematics Research Notices
VolumeAdvance Articles
Early online date25 Aug 2020
DOIs
Publication statusE-pub ahead of print - 25 Aug 2020

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