Quantum tori, mirror symmetry and deformation theory

Details Quantum tori, mirror symmetry and deformation theory Quantum tori, mirror symmetry and deformation theory

2000-11-21

arxiv.org/abs/math/0011162v3

Lett.Math.Phys. 56 (2001) 99-125

Mathematics

Quantum Algebra

Corrections to Section 4 and references added

Scientific paper

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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