2009/03/31 by Kwokwai Chan · 1 citation
Mathematics · #math.SG #math.AG #math.DG #msc:53D12 #msc:14M25 #msc:14J32
paper · pdf · doi:10.1093/imrn/rnp105
published as Int. Math. Res. Not. 2009 (2009), no. 24, 4686-4708 · v2: 20 pages; Definition 3.1 modified, a couple of examples added; to appear in IMRN
arxiv created 2009/06/30 · arxiv updated 2014/07/21
The mirror of a projective toric manifold XΣ 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 XΣ. 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.