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

Junho Lee and Naichung Conan Leung

Geometry & Topology 9 (2005) 1977–2012

arXiv: math.SG/0404537

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
Mathematical Subject Classification 2000
Primary: 53D45, 14N35
Secondary: 53D05, 14N10
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Publication
Received: 6 May 2004
Revised: 16 October 2005
Accepted: 24 April 2005
Published: 17 October 2005
Proposed: Ronald Stern
Seconded: Ronald Fintushel, Robion Kirby
Authors
Junho Lee
Department of Mathematical Sciences
Seoul National University San56-1
Shinrim-dong Kwanak-gu
Seoul 151-747
Korea
Naichung Conan Leung
Institute of Mathematical Sciences
The Chinese University of Hong Kong
Shatin
NT
Hong Kong