Counting real rational curves on K3 surfaces
Viatcheslav Kharlamov, Rares Rasdeaconu
TL;DR
This paper introduces a real analog of the Yau-Zaslow formula, enabling the counting of rational curves on K3 surfaces over the real numbers, extending complex enumerative geometry to real settings.
Contribution
It develops a new formula for counting real rational curves on K3 surfaces, complementing the existing complex Yau-Zaslow formula.
Findings
Established a real enumerative formula for K3 surfaces.
Extended complex curve counting techniques to real algebraic geometry.
Provided explicit counts for rational curves on real K3 surfaces.
Abstract
We provide a real analog of the Yau-Zaslow formula counting rational curves on surfaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Advanced Combinatorial Mathematics