An arithmetic Yau-Zaslow formula
Jesse Pajwani, Ambrus P\'al
TL;DR
This paper develops an arithmetic refinement of the Yau-Zaslow formula using motivic Euler characteristics, leading to new formulas for counting curves and related invariants in algebraic geometry.
Contribution
It introduces a motivic Euler characteristic into the Yau-Zaslow framework, extending classical results to arithmetic and real algebraic geometry contexts.
Findings
Derived an arithmetic Yau-Zaslow formula
Generalized formulas for counting real rational curves on K3 surfaces
Connected to Saito's determinant of cohomology
Abstract
We prove an arithmetic refinement of the Yau-Zaslow formula by replacing the classical Euler characteristic in Beauville's argument by a "motivic Euler characteristic", related to the work of Levine. Our result implies similar formulas for other related invariants, including a generalisation of a formula of Kharlamov and Rasdeaconu on counting real rational curves on real K3 surfaces, and Saito's determinant of cohomology.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry