Counting rational curves on K3 surfaces

Details Counting rational curves on K3 surfaces Counting rational curves on K3 surfaces

1997-01-30

arxiv.org/abs/alg-geom/9701019v1

Mathematics

Algebraic Geometry

Plain TeX, 11 pages

Scientific paper

The aim of these notes is to explain the remarkable formula found by Yau and Zaslow to express the number of rational curves on a K3 surface. Projective K3 surfaces fall into countably many families F(g) (g>0); a surface in F(g) admits a g-dimensional linear system of curves of genus g. Such a system contains a positive number, say n(g), of rational (highly singular) curves. The formula is \sum n(g) q^g = q/D((q), where D(q) = q \prod (1-q^n)^{24} is the well-known modular form of weight 12.

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