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Quadratic Euler Characteristic of Symmetric Powers of Curves

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Lukas F. Bröring
  • Anna M. Viergever

Organisationseinheiten

Externe Organisationen

  • Universität Duisburg-Essen

Details

OriginalspracheEnglisch
Aufsatznummer26
FachzeitschriftManuscripta Mathematica
Jahrgang176
Ausgabenummer2
PublikationsstatusVeröffentlicht - 20 März 2025

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 over a field of characteristic zero that the power structure on the Grothendieck-Witt ring introduced by Pajwani-Pál computes the compactly supported A^1-Euler characteristic of symmetric powers for all curves.

ASJC Scopus Sachgebiete

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Quadratic Euler Characteristic of Symmetric Powers of Curves. / Bröring, Lukas F.; Viergever, Anna M.
in: Manuscripta Mathematica, Jahrgang 176, Nr. 2, 26, 20.03.2025.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Bröring LF, Viergever AM. Quadratic Euler Characteristic of Symmetric Powers of Curves. Manuscripta Mathematica. 2025 Mär 20;176(2):26. doi: 10.1007/s00229-025-01623-0, 10.48550/arXiv.2404.16378
Bröring, Lukas F. ; Viergever, Anna M. / Quadratic Euler Characteristic of Symmetric Powers of Curves. in: Manuscripta Mathematica. 2025 ; Jahrgang 176, Nr. 2.
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