Work

A remark on the Brill–Noether theory of curves of fixed gonality

Year: 2024

Type: article

Abstract: Recently the Brill–Noether theory of curves C of both fixed genus and gonality was established. In particular, in this theory (now called the Hurwitz–Brill–Noether theory), all irreducible components of the variety of complete linear series of a fixed degree and dimension on C are obtained from the closures of certain so-called “Brill–Noether splitting loci” (loci which have a rather succinct description). In this paper, a method previously invented for the construction of some of these irreducible components is applied to get simply designed varieties inside the difference between these splitting loci and their closures, i.e., inside the boundary of the splitting loci.

Source: Archiv der Mathematik

DOI: 10.1007/s00013-024-02059-w

Author: Gerriet Martens

Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Friedrich-Alexander-Universität Erlangen-Nürnberg