Matrix factorizations from SYZ transformations

Abstract

It is known that Lagrangian torus fibers of the moment map of a toric Fano manifold $X$, equipped with flat $U(1)$-connections, are mirror to matrix factorizations of the mirror superpotential $W:\check{X}\rightarrow\bC$. Via SYZ mirror transformations, we describe how this correspondence, when $X$ is $\bP^1$ or $\bP^2$, can be explained in a geometric way.

20 pages. Dedicated to Prof. S.-T. Yau on the occasion of his 60th birthday

References in corpus (2)

• Mirror symmetry for toric Fano manifolds via SYZ transformations
• Products of Floer cohomology of torus fibers in toric Fano manifolds

Cited by in corpus (3)

• Examples of Matrix Factorizations from SYZ
• Localized mirror functor constructed from a Lagrangian torus
• Finite group actions on Lagrangian Floer theory