Toric CY hypersurfaces, fibrations and Hodge numbers

• A classification scheme for reflexive polyhedra (hep-th/9512204) relies on certain weight systems which were classified in alg-geom/9603007. In that paper it was also shown that all weights that allow transversal CY hypersurfaces also have reflexive Newton polytopes in up to 4 dimensions.
  In 4 dimensions there are 184026 weights with reflexive Newton polyhedra.
  
  
• The Newton polyhedra and Calabi-Yau hypersurfaces corresponding to these 184026 weights were analysed in hep-th/9610154. The complete information on Hodge numbers and fibration data , as well as points and vertices in the M and N lattices are encoded in this file: 2.37 MB (uncompressed 10.6 MB / subsets: 356 kB, 54 kB), consisting of 184026 lines of the form

     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
  

  encoding general data
  
  
  5 weights and their sum, the degree d.
  TS means Transverse (7555 cases) and that the Newton polytope Spans the coordinate hyperplanes (38727 lines);
  other cases are non-transverse reflexive and/or non-spanning.
  Hodge numbers are listed as h11 and h12,
  M: p v and N: p v are the numbers of points and vertices of the Newton polytope and of its dual, respectively.
  
  
  and fibration data
  
  
  P: p indicates the number p of reflexive projections, which correspond to K3 fibrations (P: - if unknown).
  F: f indicates the number f of projections onto reflexive facets. For f>0 the last f numbers denote the weights whose coordinate hyperplanes carry the K3 facets.
  
  
• The different Hodge numbers [h11 h12 chi] are listed in seperate files for
  • 7555 transverse hypersurfaces in WPs [2781 Hodge data],
  • 38727 spanning weights [8721 Hodge data] and
  • 184026 weights with reflexive Newton polyhedra [10238 Hodge data]
  
  

Weighted projective spaces and Landau-Ginzburg models

• For c=9 there are 10839 weights admitting transversal polynomials with
  n=4 (2390) / n=5 (5165) / n=6 (2567) / n=7 (669) / n=8 (47) / n=9 (1) variables (hep-th/9205004).
  7555=2390+5165 correspond to CY hypersurfaces in WP4.
• Abelian orbifolds (CY and LG) (hep-th/9211047) and
  LG models with discrete torsions (DT) (hep-th/9412033):
  Hodge numbers without (3798) / with(add. 138) D.T.