An arithmetic Yau-Zaslow formula
Algebraic Geometry
2025-12-23 v4 Number Theory
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.
Cite
@article{arxiv.2210.15788,
title = {An arithmetic Yau-Zaslow formula},
author = {Jesse Pajwani and Ambrus Pál},
journal= {arXiv preprint arXiv:2210.15788},
year = {2025}
}
Comments
63 pages. Accepted for publication in Compositio Mathematica