Quantum tori, mirror symmetry and deformation theory
Quantum Algebra
2007-05-23 v3 High Energy Physics - Theory
Algebraic Geometry
Symplectic Geometry
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.
Cite
@article{arxiv.math/0011162,
title = {Quantum tori, mirror symmetry and deformation theory},
author = {Yan Soibelman},
journal= {arXiv preprint arXiv:math/0011162},
year = {2007}
}
Comments
Corrections to Section 4 and references added