%0 Journal Article
%T Quantum corrections to the holomorphic structure of the mirror bundle along the caustic and the bifurcation locus
%A G. Marelli
%J Mathematics
%D 2007
%I arXiv
%X Given, in the Lagrangian torus fibration $R^4\to R^2$, a Lagrangian submanifold $L$, endowed with a trivial flat connection, the corresponding mirror object is constructed on the dual fibration by means of a family of Morse homologies associated to the generating function of $L$, and it is provided with a holomorphic structure. Morse homology, however, is not defined along the caustic $C$ of $L$ or along the bifurcation locus $B$, where the family does not satisfy the Morse-Smale condition. The holomorphic structure is extended to the subset $C\cup B$, except cusps, yielding the so called quantum corrections to the mirror object.
%U http://arxiv.org/abs/math/0703920v1