Quadratically Enriched Plane Curve Counting via Tropical Geometry

Abstract

We thank Jesse Pajwani for pointing out that identities in the Grothendieck-Witt ring can be checked on multiquadratic finite ´etale algebras and for his help with computations. We thank Erwan Brugall´e, Andreas Gross, Marc Levine, Dhruv Ranganathan and Kirsten Wickelgren for useful discussions. The first, second and fourth author acknowledge support by DFG-grant MA 4797/9-1. The third author acknowledges support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Centre TRR 326 Geometry and Arithmetic of Uniformized Structures, project number 444845124. The first author thanks the Universität Duisburg-Essen and the Università degli Studi di Napoli Federico II for support. Part of this work was completed while the authors stayed as Research Fellows at the Mathematisches Forschungsinstitut Oberwolfach in March 2024. We thank the institute for hosting us and for providing ideal working conditions.