Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces

@article{Abouzaid2012LagrangianFO,
  title={Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces},
  author={Mohammed Abouzaid and Denis Auroux and Ludmil Katzarkov},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2012},
  volume={123},
  pages={199-282}
}
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface H$H$ in a toric variety V$V$ we construct a Landau-Ginzburg model which is SYZ mirror to the blowup of V×C$V\times \mathbf {C}$ along H×0$H\times0$, under a positivity assumption. This construction also yields SYZ mirrors to affine conic bundles, as well as a Landau-Ginzburg model which can be… 

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