SYZ conjecture on mirrors of Lagrangian sections

Let MBM \to B and MˇB\check{M} \to B be dual torus fibrations arising in the SYZ picture, and let a Lagrangian section of MBM \to B be a Lagrangian submanifold mapping isomorphically to BB. Its mirror is an object on Mˇ\check{M}, 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 MBM \to B is a holomorphic line bundle on Mˇ\check{M}. 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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.