2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60396We 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.Corrections to Section 4 and references addedQuantum AlgebraHigh Energy Physics - TheoryAlgebraic GeometrySymplectic Geometry14J32, 17B35text