Authors: Giordano Colò
Comments: 21 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 textitalmost
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.