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arXiv · 1503.03816

On homological mirror symmetry of toric Calabi-Yau three-folds

Mark Gross·Diego Matessi
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Abstract

We use Lagrangian torus fibrations on the mirror $X$ of a toric Calabi-Yau threefold $\check X$ to construct Lagrangian sections and various Lagrangian spheres on $X$. We then propose an explicit correspondence between the sections and line bundles on $\check X$ and between spheres and sheaves supported on the toric divisors of $\check X$. We conjecture that these correspondences induce an embedding of the relevant derived Fukaya category of $X$ inside the derived category of coherent sheaves on $\check X$.

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BibTeXRIS

Mark Gross, Diego Matessi. 2015-03-12. On homological mirror symmetry of toric Calabi-Yau three-folds. https://doi.org/10.4310/jsg.2018.v16.n5.a3

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