Geometry & Topology, Vol. 9 (2005) Paper no. 45, pages 1977--2012.

Yau-Zaslow formula on K3 surfaces for non-primitive classes

Junho Lee, Naichung Conan Leung

Abstract. We compute the genus zero family Gromov-Witten invariants for K3 surfaces using the topological recursion formula and the symplectic sum formula for a degeneration of elliptic K3 surfaces. In particular we verify the Yau-Zaslow formula for non-primitive classes of index two.

Keywords. Family Gromov-Witten invariants, Yau-Zaslow formula, symplectic sum formula, topological recursion relation, K3 surface

AMS subject classification. Primary: 53D45, 14N35. Secondary: 53D05, 14N10.

E-print: arXiv:math.SG/0404537

DOI: 10.2140/gt.2005.9.1977

Submitted to GT on 06 May 2004. (Revised 16 October 2005.) Paper accepted 24 April 2005. Paper published 17 October 2005.

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Junho Lee, Naichung Conan Leung
Department of Mathematical Sciences, Seoul National University San56-1
Shinrim-dong Kwanak-gu, Seoul 151-747, Korea
Institute of Mathematical Sciences
The Chinese University of Hong Kong, Shatin, NT, Hong Kong

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