Matrix factorizations from SYZ transformations

Details Matrix factorizations from SYZ transformations Matrix factorizations from SYZ transformations

2010-06-19

arxiv.org/abs/1006.3832v1

Mathematics

Symplectic Geometry

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

Scientific paper

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.

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