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Calabi-Yau modular forms in limit: Elliptic Fibrations

Babak Haghighat Hossein Movasati Shing-Tung Yau

Algebraic Geometry mathscidoc:1912.43627

arXiv preprint arXiv:1511.01310, 2015.11
We study the limit of Calabi-Yau modular forms, and in particular, those resulting in classical modular forms. We then study two parameter families of elliptically fibred Calabi-Yau fourfolds and describe the modular forms arising from the degeneracy loci. In the case of elliptically fibred Calabi-Yau threefolds our approach gives a mathematical proof of many observations about modularity properties of topological string amplitudes starting with the work of Candelas, Font, Katz and Morrison. In the case of Calabi-Yau fourfolds we derive new identities not computed before.
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@inproceedings{babak2015calabi-yau,
  title={Calabi-Yau modular forms in limit: Elliptic Fibrations},
  author={Babak Haghighat, Hossein Movasati, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204539400967191},
  booktitle={arXiv preprint arXiv:1511.01310},
  year={2015},
}
Babak Haghighat, Hossein Movasati, and Shing-Tung Yau. Calabi-Yau modular forms in limit: Elliptic Fibrations. 2015. In arXiv preprint arXiv:1511.01310. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204539400967191.
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