The number of rational curves on K3 surfaces

Details The number of rational curves on K3 surfaces The number of rational curves on K3 surfaces

2006-02-13

arxiv.org/abs/math/0602280v2

Mathematics

Algebraic Geometry

15 pages, added references, to appear in Asian J. Math

Scientific paper

Let X be a K3 surface with a primitive ample divisor H, and let
$\beta=2[H]\in H_2(X, \mathbf Z)$. We calculate the Gromov-Witten type
invariants $n_{\beta}$ by virtue of Euler numbers of some moduli spaces of
stable sheaves. Eventually, it verifies Yau-Zaslow formula in the non primitive
class $\beta$.

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