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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

# BigObject RationalDivisorClassGroup

from application fulton

The class group Cl(X) of Weil divisors on the toric variety defined by the fan is a finitely generated abelian group of rank N_RAYS-DIM. It usually contains torsion. The rational divisor class group is the tensor product of Cl(X) with Q over Z. This group is torsion free and corresponds to the Picard group if the variety is non-singular.

### Algebraic Geometry

Properties from algebraic geometry.

LIFTING

Lifts a divisor in the class group onto a divisor on the fan.

Type:
Matrix<Integer,NonSymmetric>

PROJECTION

Maps a divisor on the variety onto its representation in the class group.

Type:
Matrix<Integer,NonSymmetric>

• documentation/latest/fulton/rationaldivisorclassgroup.txt