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arxiv: 1006.3832 · v1 · pith:JH2APPU6new · submitted 2010-06-19 · 🧮 math.SG · math.AG

Matrix factorizations from SYZ transformations

classification 🧮 math.SG math.AG
keywords mirrorfactorizationsmatrixtransformationscheckconnectionscorrespondencedescribe
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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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