Will Reynold's Computations

My PhD student Will Reynolds has computed (using the Macaulay2 package NormalToricVarieties) the primitive relations of all of the smooth toric Fano varieties of dimensions 4 and 5. This data is available in the files below.

The '.txt' files contain the data in a format which can be loaded directly into Macaulay2. The '.pdf' documents provide a more human-readable version.

In this Macaulay2 data, primRel_(d, i) is the list of primitive relations of smoothFanoToricVariety(d, i), with exactly one exception: smoothFanoToricVariety(5, 0) is a duplicate of the projective space of dimension 5, which is also smoothFanoToricVariety(5, 865). This duplication is corrected in the data provided here: primRel_(5, 0) is the list of primitive relations of the correct variety, namely entry 148 in the Graded Ring Database, whose fan was obtained in M2 by defining this variety as the normalToricVariety corresponding to the dual polytope given in the Graded Ring Database.

Primitive relations of smooth Toric Fano 4 folds as a text file.

Primitive relations of smooth Toric Fano 4 folds as a pdf file.

Primitive relations of smooth Toric Fano 5 folds as a text file.

Primitive relations of smooth Toric Fano 5 folds as a pdf file.