Prym-Brill-Noether loci of special curves

Steven Creech; Yoav Len; Caelan Ritter; Derek Wu

doi:10.1093/imrn/rnaa207

Prym-Brill-Noether loci of special curves

Steven Creech, Yoav Len^*, Caelan Ritter, Derek Wu

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	41
Journal	International Mathematics Research Notices
Volume	Advance Articles
Early online date	25 Aug 2020
DOIs	https://doi.org/10.1093/imrn/rnaa207
Publication status	E-pub ahead of print - 25 Aug 2020

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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
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Yoav Len
- yoav.lenst-andrews.acuk
- Pure Mathematics - Lecturer in Pure Mathematics
Person: Academic

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title = "Prym-Brill-Noether loci of special curves",

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.",

author = "Steven Creech and Yoav Len and Caelan Ritter and Derek Wu",

note = "Funding: 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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AU - Creech, Steven

AU - Len, Yoav

AU - Ritter, Caelan

AU - Wu, Derek

N1 - Funding: 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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N2 - 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.

AB - 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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DO - 10.1093/imrn/rnaa207

M3 - Article

SN - 1073-7928

VL - Advance Articles

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

ER -

Prym-Brill-Noether loci of special curves

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