Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Counting elliptic curves in $ \mathrm{K3}$ surfaces


Authors: Junho Lee and Naichung Conan Leung
Journal: J. Algebraic Geom. 15 (2006), 591-601
DOI: https://doi.org/10.1090/S1056-3911-06-00439-5
Published electronically: May 2, 2006
MathSciNet review: 2237262
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Abstract | References | Additional Information

Abstract: We compute the genus $ g=1$ family GW-invariants of K3 surfaces for non-primitive classes. These calculations verify the Göttsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships among various generating functions.


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Additional Information

Junho Lee
Affiliation: 921 D Cherry Lane, East Lansing, Michigan 48823
Email: leejunho@msu.edu

Naichung Conan Leung
Affiliation: Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
Email: leung@ims.cuhk.edu.hk

DOI: https://doi.org/10.1090/S1056-3911-06-00439-5
Received by editor(s): April 29, 2004
Received by editor(s) in revised form: October 9, 2005
Published electronically: May 2, 2006
Additional Notes: The second author is partially supported by NSF/DMS-0103355, CUHK/2060275, and CUHK/2160256.

American Mathematical Society