Authors: Giordano Colò
Comments: 22 Pages.
We try to give a formulation of Strominger-Yau-Zaslow conjecture on mirror symmetry by studying the singularities of special Lagrangian submanifolds of 3-dimensional Calabi-Yau manifolds. In this paper we’ll give the description of the boundary of the moduli space of special Lagrangian manifolds. We do this by introducing special Lagrangian cones in the more general Kähler manifolds. Then we can focus on the almost Calabi-Yau manifolds. We consider the behaviour of the Lagrangian manifolds near the conical singular points to classify them according to the way they are approximated from the asymptotic cone. Then we analyze their deformations in Calabi-Yau manifolds.