Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
Abstract
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the StromingerYauZaslow (SYZ) conjecture. Given a hypersurface $H$ in a toric variety $V$ we construct a LandauGinzburg model which is SYZ mirror to the blowup of $V\times\mathbb{C}$ along $H\times 0$, under a positivity assumption. This construction also yields SYZ mirrors to affine conic bundles, as well as a LandauGinzburg model which can be naturally viewed as a mirror to $H$. The main applications concern affine hypersurfaces of general type, for which our results provide a geometric basis for various mirror symmetry statements that appear in the recent literature. We also obtain analogous results for complete intersections.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1205.0053
 Bibcode:
 2012arXiv1205.0053A
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Geometry
 EPrint:
 83 pages