Tropical methods in Hurwitz-Brill-Noether theory

Kaelin Cook-Powell, David Jensen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Splitting type loci are the natural generalizations of Brill-Noether varieties for curves with a distinguished map to the projective line. We give a tropical proof of a theorem of H. Larson, showing that splitting type loci have the expected dimension for general elements of the Hurwitz space. Our proof uses an explicit description of splitting type loci on a certain family of tropical curves. We further show that these tropical splitting type loci are connected in codimension one, and describe an algorithm for computing their cardinality when they are zero-dimensional. We provide a conjecture for the numerical class of splitting type loci, which we confirm in a number of cases.

Original languageEnglish
Article number108199
JournalAdvances in Mathematics
Volume398
DOIs
StatePublished - Mar 26 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

  • Brill-Noether theory
  • Gonality
  • Hurwitz spaces
  • Tropical geometry

ASJC Scopus subject areas

  • General Mathematics

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