1997/01/29 by Maximilian Kreuzer, M. Kreuzer, Harald Skarke +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Geometry and complex manifolds #alg-geom #hep-th #math.AG
paper · pdf · doi:10.1016/s0393-0440(97)00059-4
published as J.Geom.Phys. 26 (1998) 272-290 · 20 pages, LaTeX2e
arxiv created 1997/01/29 · openalex publication_date 1998/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a general scheme for identifying fibrations in the framework of toric geometry and provide a large list of weights for Calabi--Yau 4-folds. We find 914,164 weights with degree d≤150 whose maximal Newton polyhedra are reflexive and 525,572 weights with degree d≤4000 that give rise to weighted projective spaces such that the polynomial defining a hypersurface of trivial canonical class is transversal. We compute all Hodge numbers, using Batyrev's formulas (derived by toric methods) for the first and Vafa's fomulas (obtained by counting of Ramond ground states in N=2 LG models) for the latter class, checking their consistency for the 109,308 weights in the overlap. Fibrations of k-folds, including the elliptic case, manifest themselves in the N lattice in the following simple way: The polyhedron corresponding to the fiber is a subpolyhedron of that corresponding to the k-fold, whereas the fan determining the base is a linear projection of the fan corresponding to the k-fold.