Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
M Abouzaid, D Auroux, L Katzarkov�- arXiv preprint arXiv:1205.0053, 2012 - arxiv.org
M Abouzaid, D Auroux, L Katzarkov
arXiv preprint arXiv:1205.0053, 2012•arxiv.orgWe 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 $ in a toric variety $ V $ we construct a Landau-
Ginzburg 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 Landau-Ginzburg model which can be naturally viewed as a mirror to�…
noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ)
conjecture. Given a hypersurface $ H $ in a toric variety $ V $ we construct a Landau-
Ginzburg 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 Landau-Ginzburg model which can be naturally viewed as a mirror to�…
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 in a toric variety we construct a Landau-Ginzburg model which is SYZ mirror to the blowup of along , under a positivity assumption. This construction also yields SYZ mirrors to affine conic bundles, as well as a Landau-Ginzburg model which can be naturally viewed as a mirror to . 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.
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