Calabi--Yau Operators

Duco van Straten

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arXiv · 1704.00164

Calabi--Yau Operators

Duco van Straten

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Abstract

Motivated by mirror symmetry of one-parameter models, an interesting class of Fuchsian differential operators can be singled out, the so-called Calabi--Yau operators, introduced by Almkvist and Zudilin. They conjecturally determine $Sp(4)$-local systems that underly a $\mathbb{Q}$-VHS with Hodge numbers \[h^{3 0}=h^{2 1}=h^{1 2}=h^{0 3}=1\] and in the best cases they make their appearance as Picard--Fuchs operators of families of Calabi--Yau threefolds with $h^{12}=1$ and encode the numbers of rational curves on a mirror manifold with $h^{11}=1$. We review some of the striking properties of this rich class of operators.

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Duco van Straten. 2017-04-01. Calabi--Yau Operators. https://arxiv.org/abs/1704.00164

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