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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（4）
• 页码范围: 613-636
• 页数: 24页
• 语种: 英文
• DOI: 10.1007/s11425-015-0722-2

摘要

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.