Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holomorphic line bundles on projective toric manifolds from Lagrangian
  sections of their mirrors by SYZ transformations   The mirror of a projective toric manifold $X_\Sigma$ 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 $X_\Sigma$. 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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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga