An arithmetic Yau–Zaslow formula
Abstract
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 Răsdeaconu on counting real rational curves on real K3 surfaces, and Saito’s determinant of cohomology.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 4
- Pages
- 792–851
- Publication date
- 1 April 2026
- Language
- EN