The number of rational curves on K3 surfaces

Baosen Wu

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The number of rational curves on K3 surfaces

Baosen Wu

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Abstract

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

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Baosen Wu. 2006-11-15. The number of rational curves on K3 surfaces. https://arxiv.org/abs/math/0602280

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