SYZ conjecture on mirrors of Lagrangian sections
SYZ conjecture on mirrors of Lagrangian sections
Let and be dual torus fibrations arising in the SYZ picture, and let a Lagrangian section of be a Lagrangian submanifold mapping isomorphically to . Its mirror is an object on , and a holomorphic line bundle is a line bundle equipped with a holomorphic structure. SYZ section-to-line-bundle conjecture. The mirror of a Lagrangian section of is a holomorphic line bundle on . This is described in the paper as a folkloric observation and is the part of the SYZ intuition used for toric varieties; the supplied text gives no resolution status.
Sources & referencesView supporting material
Primary source
Mohammed Abouzaid, “Morse Homology, Tropical Geometry, and Homological Mirror Symmetry for Toric Varieties”, arXiv:math/0610004 (2009).
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