Communications in Number Theory and Physics
Volume 11 (2017)
Calabi-Yau modular forms in limit: Elliptic fibrations
Pages: 879 – 912
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.
modular forms, Hodge filtration, Picard–Fuchs system
2010 Mathematics Subject Classification
14J15, 14N35, 32G20
Paper received on 12 February 2016.
Paper accepted on 13 July 2017.