Holomorphic Line Bundles on Projective Toric Manifolds from Lagrangian Sections of their Mirrors by SYZ Transformations
Holomorphic Line Bundles on Projective Toric Manifolds from Lagrangian Sections of their Mirrors by SYZ Transformations
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通过 SYZ 变换从镜子的拉格朗日截面射影环面流形上的全纯线束
DOI：
10.1093/imrn/rnp105
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发表时间：
2009
影响因子：
1
通讯作者：
Kwokwai Chan
中科院分区：
文献类型：
--
作者：
Kwokwai Chan
射影环流形的镜像由Landau-Ginzburg模型（Y， W）给出。我们在（Y， W）中引入了一类拉格朗日子流形，并证明了在SYZ镜像变换下，它们可以被变换为全纯线束上的环不变厄密度量。通过这种几何对应关系，我们还确定了埃尔米特-爱因斯坦度量的镜像，这些镜像由不同的拉格朗日截面给出，其势满足某些拉普拉斯型方程。
The mirror of a projective toric manifold 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 . 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.