Calabi-Yau 4-folds and toric fibrations

Maximilian Kreuzer, Harald Skarke
1998 Journal of Geometry and Physics  
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
more » ... 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.
doi:10.1016/s0393-0440(97)00059-4 fatcat:q53dyqrfzvhdbfxamljx3jz4fm