Strings on Calabi—Yau spaces and toric geometry

2001/03/31 by Maximilian Kreuzer
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Finite geometry #Geometry and complex manifolds #Range (aeronautics) #String (physics) #Toric variety #Upper and lower bounds #hep-th

paper · pdf · doi:10.1016/s0920-5632(01)01541-9

published as Nucl.Phys.Proc.Suppl.102:87-93,2001 · error in Hodge data of complete intersections corrected, published in Nucl.Phys. B Conf. Suppl. 102 (2001) 87

openalex publication_date 2001/09/01 · arxiv created 2002/10/12 · arxiv updated 2011/07/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

After a brief introduction into the use of Calabi--Yau varieties in string dualities, and the role of toric geometry in that context, we review the classification of toric Calabi-Yau hypersurfaces and present some results on complete intersections. While no proof of the existence of a finite bound on the Hodge numbers is known, all new data stay inside the familiar range h₁₁+h₁₂≤ 502.

Citations

• Vacuum configurations for superstrings
• String theory dynamics in various dimensions
• ADE string vacua with discrete torsion
• Complete intersection Calabi-Yau manifolds
• Evidence for F-theory
• Mirror symmetry is T-duality
• Massless black holes and conifolds in string theory
• A generalized construction of mirror manifolds
• Black hole condensation and the unification of string vacua
• No mirror symmetry in Landau-Ginzburg spectra!
• Geometric singularities and enhanced gauge symmetries
• Dirichlet Branes and Ramond-Ramond Charges
• Exact results for N = 2 compactifications of heterotic strings