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PreprintCC BY 4.0arXiv

Pointed Hurwitz--Brill--Noether theory

  • Andrei Bud
  • Richard Haburcak
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Abstract

We study the geometry of Hurwitz--Brill--Noether spaces with vanishing conditions at a totally ramified point. Degeneration to a curve with an elliptic tail simplifies the combinatorics of Larson, Larson--Larson--Vogt, and Aggarwal, giving inductive proofs of Aggarwal's results in the one-point setting, and yields an efficient recursion for the algebraic Euler characteristics. Finally, when the expected dimension is negative, we give a numerical criterion ensuring the universal Hurwitz--Brill--Noether locus admits a component of expected relative dimension, generically finite over its image in the Hurwitz space, analogous to the existing results of Pflueger and Teixidor i Bigas for classical Brill--Noether loci.

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Cite

BibTeXRIS
BibTeX
@misc{bud2026pointed,
  title = {{Pointed Hurwitz--Brill--Noether theory}},
  author = {Andrei Bud and Richard Haburcak},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38023},
  eprint = {2610.38023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38023},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Pointed Hurwitz--Brill--Noether theory
AU  - Andrei Bud
AU  - Richard Haburcak
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.38023
UR  - https://arxiv.org/abs/2610.38023
AB  - We study the geometry of Hurwitz--Brill--Noether spaces with vanishing conditions at a totally ramified point. Degeneration to a curve with an elliptic tail simplifies the combinatorics of Larson, Larson--Larson--Vogt, and Aggarwal, giving inductive proofs of Aggarwal's results in the one-point setting, and yields an efficient recursion for the algebraic Euler characteristics. Finally, when the expected dimension is negative, we give a numerical criterion ensuring the universal Hurwitz--Brill--Noether locus admits a component of expected relative dimension, generically finite over its image in the Hurwitz space, analogous to the existing results of Pflueger and Teixidor i Bigas for classical Brill--Noether loci.
ER  -