In arXiv:1204.1181
a classification scheme for reflexive Gorenstein cones was presented.
An essential role for that scheme is played by basic weight systems,
i.e. weight systems containing no weights of 1/2 or 1 and no two weights whose
sum is 1.
We use the following notation:
-
d ... the dimension of the cone,
-
r ... the index of the cone,
-
dCY = d - 2r ... the "Calabi-Yau-dimension" of the cone,
-
qi = ni/k ... the weights.
The files presented below contain lines of the form
k n1 ... nd M: # # N: # # H: ...
if the cone determined by the weight system is reflexive, and of
the form
k n1 ... nd M: # # F: #
otherwise, where
-
k n1 ... nd encodes the weights as
qi = ni/k,
-
M: # # gives the numbers of lattice points and vertices of the
support of the cone,
-
N: # # gives the numbers of lattice points and vertices of the
support of the dual cone,
-
H: ... gives the "stringy Hodge numbers" in the format
h11 ... h1,dCY-1 [Euler number]
(non-standard h0i),
where "non-standard h0i" indicates any h0i's that
do not follow the standard pattern
h00 = hdCYdCY = 1,
h0i = 0 for 0 < i < dCY,
-
F: # gives the number of facets of the support of the cone.
Weight systems for (d,r) with half-integer r are listed as the weight systems
of type (d+1,r+1/2) that are obtained by adding one weight of 1/2;
e.g. (1/6, 1/6, 1/6) of type (3, 1/2) becomes (1/6, 1/6, 1/6, 1/2) of type
(4, 1) etc.
The basic weight systems for dCY = 2 are listed in the following files:
d=6, r=2
(1)