Calabi-Yau threefold hypersurfaces in toric varieties
A complete list of the Hodge data of Calabi-Yau threefolds described by
hypersurfaces in toric varieties has been obtained
by Avram, Kreuzer, Mandelberg and Skarke in ref.
This paper also contains a fibration flags for those threefolds
that are K3 fibrations.
The data of the 184026 toric weight configurations
analyzed in this paper is contained in the following
2.4mb file .
The notation of the list
1 1 1 1 1 5=d TS H: 1 101 M:126 5 N: 6 5 P:0 F:0
3 4 5 6 8 26=d rS H:14 24 M: 32 14 N:19 10 P:- F:1 6
1 3 3 10 14 31=d Tn H:14 106 M:143 9 N:21 7 P:0 F:0
4 7 7 10 12 40=d rn H:28 16 M: 23 7 N:25 6 P:3 F:2 7 12
indicates the following:
- the first 5 entries describe the weights, which add up to the sixth,
- T stands for transverse (there are 7,555 configuration of
- S indicates that the polytope spans the coodinate hyperplanes
(this applies to 38727 configurations).
- the two numbers following the symbol H are the Hodge
numbers of the corresponding Calabi-Yau threefold.
- M: p n denote the number of points and vertices
for the Newton polytope M and its dual N
- P: n denotes the number of possible reflexive projections
of the polytope, describing the number of possible K3 fibrations
(an `-' indicates that this number is not known).
- F: n ndicates the number f of projections onto reflexive facets. For f>0 the last f
numbers denote the weights whose coordinate hyperplanes carry the K3 faces.