Work

Quadratic Euler characteristic of symmetric powers of curves

Year: 2025

Type: article

Abstract: We compute the quadratic Euler characteristic of the symmetric powers of a smooth, projective curve over any field k that is not of characteristic two, using the Motivic Gauss–Bonnet Theorem of Levine–Raksit. As an application, we show that the power structure on the Grothendieck–Witt ring introduced by Pajwani–Pál computes the compactly supported $${\mathbb {A}}^1$$ A 1 -Euler characteristic of symmetric powers for all curves.

Source: manuscripta mathematica

DOI: 10.1007/s00229-025-01623-0

Authors: Lukas F. Bröring, Anna M. Viergever

Institutions: University of Duisburg-Essen, Leibniz University Hannover

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: European Commission, Deutsche Forschungsgemeinschaft, Gottfried Wilhelm Leibniz Universität Hannover, HORIZON EUROPE European Research Council