Eisenstein type series for Calabi-Yau varieties

Details Eisenstein type series for Calabi-Yau varieties Eisenstein type series for Calabi-Yau varieties

2010-07-23

arxiv.org/abs/1007.4181v2

Mathematics

Algebraic Geometry

22 pages

Scientific paper

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 $q$-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.

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