Torus fibrations of Calabi-Yau hypersurfaces in toric varieties

DOI10.1215/S0012-7094-00-10124-XzbMath0957.14031arXivmath/9806091MaRDI QIDQ1976044

Ilia Zharkov

Publication date: 20 March 2001

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9806091

zbMATH Keywords

toric varietiesmirror symmetrymoment mapCalabi-Yau hypersurfacesLagrangian fibrationsStrominger-Yau-Zaslow conjecture

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) String and superstring theories in gravitational theory (83E30) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Fibrations, degenerations in algebraic geometry (14D06) Hypersurfaces and algebraic geometry (14J70)

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Cites Work

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• Branes and toric geometry
• Kaehler structures on toric varieties
• Mirror symmetry via 3-tori for a class of Calabi-Yau threefolds
• Some examples of special Lagrangian tori
• Mirror symmetry is \(T\)-duality
• Special Lagrangian Fibrations I: Topology
• The Geometry Underlying Mirror Symmetry
• The Monomial-Divisor Mirror Map
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Recent developments in toric geometry