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Quadratic Euler Characteristic of Symmetric Powers of Curves

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Lukas F. Bröring
  • Anna M. Viergever

Research Organisations

External Research Organisations

  • University of Duisburg-Essen
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Details

Original languageEnglish
Article number26
JournalManuscripta Mathematica
Volume176
Issue number2
Publication statusPublished - 20 Mar 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-P\'al computes the compactly supported $\mathbb{A}^1$-Euler characteristic of symmetric powers for all curves.

Keywords

    math.AG, 14G27, 14N10, 14F42

ASJC Scopus subject areas

Cite this

Quadratic Euler Characteristic of Symmetric Powers of Curves. / Bröring, Lukas F.; Viergever, Anna M.
In: Manuscripta Mathematica, Vol. 176, No. 2, 26, 20.03.2025.

Research output: Contribution to journal › Article › Research › peer review

Bröring LF, Viergever AM. Quadratic Euler Characteristic of Symmetric Powers of Curves. Manuscripta Mathematica. 2025 Mar 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 ; Vol. 176, No. 2.
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