Gauss-Manin connection in disguise: Calabi-Yau modular forms 9781571463432

This book intends to construct a theory of modular forms for families of Calabi-Yau threefolds with Hodge numbers of the

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English Pages 180 [198] Year 2017

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Gauss-Manin connection in disguise: Calabi-Yau modular forms 9781571463432

Table of contents :
Contents
1. Introduction
2. Summary of results and computations
3. Moduli of enhanced mirror quintics
4. Topology and Periods
5. Formal power series solutions
6. Topological String Partition Functions
7. Holomorphic differential Calabi-Yau modular
forms
8. Non-holomorphic differential Calabi-Yau
modular forms
9. BCOV holomorphic anomaly equation
10. Calabi-Yau modular forms
11. Problems
A. Second order linear differential equations
B. Metric
C. Integrality properties of Calabi-Yau modular
forms
D. Variations of Hodge structures, Lyapunov
exponents and Kontsevich’s formula
References

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