Mirror Symmetry for Toric Branes on Compact Hypersurfaces

Understand

We use toric geometry to study open string mirror symmetry on compact Calabi-Yau manifolds.

• For a mirror pair of toric branes on a mirror pair of toric hypersurfaces we derive a canonical hypergeometric system of differential equations, whose solutions determine the open/closed string mirror maps and the partition functions for spheres and discs.
• We define a linear sigma model for the brane geometry and describe a correspondence between dual toric polyhedra and toric brane geometries.
• The method is applied to study examples with obstructed and classically unobstructed brane moduli at various points in the deformation space.