Geometry & Topology

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

Junho Lee and Naichung Conan Leung

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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.

Article information

Source
Geom. Topol., Volume 9, Number 4 (2005), 1977-2012.

Dates
Received: 6 May 2004
Revised: 16 October 2005
Accepted: 24 April 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799673

Digital Object Identifier
doi:10.2140/gt.2005.9.1977

Mathematical Reviews number (MathSciNet)
MR2175162

Zentralblatt MATH identifier
1088.53059

Subjects
Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D05: Symplectic manifolds, general 14N10: Enumerative problems (combinatorial problems)

Keywords
family Gromov–Witten invariants Yau–Zaslow formula symplectic sum formula topological recursion relation K3 surface

Citation

Lee, Junho; Leung, Naichung Conan. Yau–Zaslow formula on K3 surfaces for non-primitive classes. Geom. Topol. 9 (2005), no. 4, 1977--2012. doi:10.2140/gt.2005.9.1977. https://projecteuclid.org/euclid.gt/1513799673


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