Abstract
In this article we calculate the Picard–Fuchs equation of hypersurfaces defined by certain one-parameter families associated to invertible polynomials. For this we deduce the Picard–Fuchs equation from the GKZ system. As consequences of our work and facts from the literature, we show a relation between the Picard–Fuchs equation, the Poincaré series and the monodromy in the space of period integrals.
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Acknowledgements
This work was supported in part by DFG-RTG 1463. This article was part of my Ph.D. thesis and I would like to thank my supervisor Prof. Wolfgang Ebeling for his support. During my research I was supported by DFG RTG 1463. I would also like to thank Prof. Noriko Yui and Prof. Ragnar-Olaf Buchweitz, who were gave me input during my stay at the Fields Institute in Toronto. In addition I would like to thank the referee for helpful comments.
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Gährs, S. (2013). Picard–Fuchs Equations of Special One-Parameter Families of Invertible Polynomials. In: Laza, R., Schütt, M., Yui, N. (eds) Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds. Fields Institute Communications, vol 67. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6403-7_9
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