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Quantum tori, mirror symmetry and deformation theory

Yan Soibelman
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Abstract

We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of abelian varieties this approach gives quantum tori as a non-commutative boundary of the moduli space. Relations to mirror symmetry, modular forms and deformation theory are discussed.

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Yan Soibelman. 2000-11-23. Quantum tori, mirror symmetry and deformation theory. https://arxiv.org/abs/math/0011162

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