String Dualities and Toric Geometry: An Introduction
arXiv:hep-th/9806059 · doi:10.1016/S0960-0779(98)00161-1
Abstract
This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in terms of homogeneous coordinates, stressing the analogy with weighted projective spaces. We try to give both intuitive pictures and precise rules that should enable the reader to work with the concepts presented here.
17 pages, Latex, 7 figures, invited paper to appear in the special issue of the Journal of Chaos, Solitons and Fractals on "Superstrings, M, F, S, ... Theory" (M.S. El Naschie and C. Castro, editors)
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Cited by in corpus (12)
- Toric K3-Fibred Calabi-Yau Manifolds with del Pezzo Divisors for String Compactifications
- An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts
- PALP - a User Manual
- Type IIB flux vacua from G-theory I
- Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
- On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
- NS5-Branes and Line Bundles in Heterotic/F-Theory Duality
- F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
- Mirror symmetry and elliptic Calabi-Yau manifolds
- Symplectic gauge invariant reformulation of a free particle system on toric geometry
- Algebro-geometrical orientifolds and IR dualities
- Effective Superpotentials of Type II D-brane/F-theory on Compact Complete Intersection Calabi-Yau Threefolds