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Quantum corrections to the holomorphic structure of the mirror bundle along the caustic and the bifurcation locus

G. Marelli
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Abstract

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.

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G. Marelli. 2007-03-30. Quantum corrections to the holomorphic structure of the mirror bundle along the caustic and the bifurcation locus. https://arxiv.org/abs/math/0703920

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