Prym-Brill-Noether loci of special curves
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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.
Creech , S , Len , Y , Ritter , C & Wu , D 2020 , ' Prym-Brill-Noether loci of special curves ' , International Mathematics Research Notices , vol. Advance Articles . https://doi.org/10.1093/imrn/rnaa207
International Mathematics Research Notices
Copyright © The Author(s) 2020. Published by Oxford University Press. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1093/imrn/rnaa207
DescriptionFunding: This research was conducted at the Georgia Institute of Technology with the support of RTG grant GR10004614 and REU grant GR10004803.
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