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

Mohammed Abouzaid, Denis Auroux, Ludmil Katzarkov

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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 (Formula presented.) in a toric variety (Formula presented.) we construct a Landau-Ginzburg model which is SYZ mirror to the blowup of (Formula presented.) along (Formula presented.), 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 (Formula presented.). 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.

Original languageEnglish (US)
Pages (from-to)1-84
Number of pages84
JournalPublications Mathematiques de l'Institut des Hautes Etudes Scientifiques
DOIs
StateAccepted/In press - Mar 2 2016
Externally publishedYes

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Mirror Symmetry
Toric Varieties
Fibration
Hypersurface
Ginzburg-Landau Model
Mirror
Complete Intersection
Positivity
Blow-up
Bundle
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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