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arXiv · 0903.1164

Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations

Kwokwai Chan
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Abstract

The mirror of a projective toric manifold $X_Σ$ is given by a Landau-Ginzburg model $(Y,W)$. We introduce a class of Lagrangian submanifolds in $(Y,W)$ and show that, under the SYZ mirror transformation, they can be transformed to torus-invariant hermitian metrics on holomorphic line bundles over $X_Σ$. Through this geometric correspondence, we also identify the mirrors of Hermitian-Einstein metrics, which are given by distinguished Lagrangian sections whose potentials satisfy certain Laplace-type equations.

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Kwokwai Chan. 2009-06-30. Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations. https://doi.org/10.1093/imrn%2Frnp105

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