Counting elliptic curves in 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 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.