2000/11/23 by Yan Soibelman
Mathematics · Physics and Astronomy · #math.QA #hep-th #math.AG #math.SG #msc:14J32 #msc:17B35
published as Lett.Math.Phys. 56 (2001) 99-125 · Corrections to Section 4 and references added
arxiv created 2000/11/23 · arxiv updated 2009/11/30
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.