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Calabi-Yau data
    obtained by M. Kreuzer, H. Skarke and collaborators.
More data and programs can be found on the CY pages maintained by
Sheldon KATZ (Oklahoma/USA) and Rolf SCHIMMRIGK (Bonn/Germany)


Weight systems for Calabi-Yau 4-folds

Toric CY hypersurfaces, fibrations and Hodge numbers

  • Our classification scheme for reflexive polyhedra (hep-th/9512204) relies on certain weight systems which were computed in alg-geom/9603007. In that paper it was also shown that all weights that allow transversal CY hypersurfaces 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 information on Hodge and fibration data, as well as numbers of points and vertices in the M and N lattices, are encoded in a big file: 2.37 MB (uncompressed 10.6 MB / subsets with lowest and highest degrees: 356 kB , 54 kB). The files contain 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 lines) 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

Weighted projective spaces and Landau-Ginzburg models

Other CY sites: Sheldon KATZ (Oklahoma/USA), Rolf SCHIMMRIGK (Bonn/Germany)

The data on this CY page are maintained by Maximilian KREUZER and Harald SKARKE

Comments / problems / questions / suggestions: send an
e-mail to Maximilian Kreuzer or an
e-mail to Harald Skarke