CalabiYau Operators
Abstract
Motivated by mirror symmetry of oneparameter models, an interesting class of Fuchsian differential operators can be singled out, the socalled CalabiYau 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 PicardFuchs operators of families of CalabiYau 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2017
 DOI:
 10.48550/arXiv.1704.00164
 arXiv:
 arXiv:1704.00164
 Bibcode:
 2017arXiv170400164V
 Keywords:

 Mathematics  Algebraic Geometry;
 14J32;
 32S40
 EPrint:
 This paper of expository character is an extended written version of a talk given at the conference "Uniformization, RiemannHilbert Correspondence, CalabiYau Manifolds, and PicardFuchs Equations" held 13.18.07.2015 at the MittagLeffler Institute which was organised by L. Ji and S.T. Yau and will appear in the conference proceedings