Special divisors on real trigonal curves

Akyar T.

ADVANCES IN GEOMETRY, vol.2025, pp.463-473, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2025
  • Publication Date: 2025
  • Doi Number: 10.1515/advgeom-2025-0026
  • Journal Name: ADVANCES IN GEOMETRY
  • Journal Indexes: Scopus, Aerospace Database, Science Citation Index Expanded (SCI-EXPANDED), Academic Search Premier, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.463-473
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper we examine the topology of Brill-Noether varieties associated to real trigonal curves. More precisely, we aim to count the connected components of the real locus of the varieties parametrizing linear systems of degree $d$ and dimension at least $r$. We do this count when the relations $m=g-d+r-1\leq d-2r-1$ are satisfied, where $m$ is the Maroni invariant and $g$ is the genus of the curve.