Eisenstein type series for Calabi-Yau varieties
arXiv:1007.4181 · doi:10.1016/j.nuclphysb.2011.01.028
Abstract
In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the -expansion form and the Yukawa coupling turns out to be rational in these functions. This is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.
22 pages
References in corpus (6)
- Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
- Polynomial Structure of the (Open) Topological String Partition Function
- Integrality of instanton numbers and p-adic B-model
- Topological Strings and (Almost) Modular Forms
- Monodromy calculatons of fourth order equations of Calabi-Yau type
- On the integrality of the Taylor coefficients of mirror maps
Cited by in corpus (5)
- Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
- Differential Rings from Special Kähler Geometry
- Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
- Modular-type functions attached to mirror quintic Calabi-Yau varieties
- Darboux-Halphen-Ramanujan Vector Field on a Moduli of Calabi-Yau Manifolds