Work

Prym–Brill–Noether theory for ramified double covers

Year: 2026

Type: article

Abstract: We initiate the study of Prym–Brill–Noether theory for ramified double covers, extending several key results from classical Prym–Brill–Noether theory to this new framework. In particular, we improve Kanev’s results on the dimension of pointed Prym–Brill–Noether loci for ramified double covers. Additionally, we compute the dimension of twisted Prym–Brill–Noether loci with vanishing conditions at points, thus extending the results of Tarasca. Furthermore, we compute the class of the twisted Prym–Brill–Noether loci inside (a translation of) the Prym variety, thus extending the results of de Concini and Pragacz to ramified double covers. Finally, we prove that a generic Du Val curve is Prym–Brill–Noether general.

Source: Documenta Mathematica

DOI: 10.4171/dm/1075

Author: Andrei Bud

Institutions: Goethe University Frankfurt, Université Toulouse III - Paul Sabatier

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Awards: G5846448348, TRR 326: Geometrie und Arithmetik uniformisierter Strukturen (GAUS)