QUEST Leibniz Research School

Quadratic Euler Characteristic of Symmetric Powers of Curves

authored by: Lukas F. Bröring, Anna M. Viergever
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.
Organisation(s): Institute of Algebraic Geometry
Type: Preprint
Publication date: 25.04.2024
Publication status: E-pub ahead of print

BibTeX

@techreport{fe57c27324814e58b66bf318a8da97d2,
title = "Quadratic Euler Characteristic of Symmetric Powers of Curves",
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",
author = "Br{\"o}ring, {Lukas F.} and Viergever, {Anna M.}",
note = "19 pages, corrected typos, improved exposition. Comments still welcome!",
year = "2024",
month = apr,
day = "25",
language = "English",
type = "WorkingPaper",
}

Last Change: 09.02.23; Dr. A. Wanner Print