Science China Mathematics

, Volume 60, Issue 4, pp 613–636 | Cite as

A conjectural formula for genus one Gromov-Witten invariants of some local Calabi-Yau n-folds



We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol’nyi-Prasad-Sommerfield (BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande.


Gromov-Witten invariant virtual localization integrality 


14N35 53D45 


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The author thanks Professor Jian Zhou for his great patience and guidance during all the time. The author also thanks Jie Yang, Huijun Fan, Huazhong Ke, Jie Zhou, Xiaobo Zhuang, and Di Yang for helpful discussions. The author especially thanks Jie Zhou for carefully reading an earlier version of the introduction and giving suggestions.


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina

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