Available versions of this document: latest release, release 4.0, release 3.6, release 3.5, nightly master

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.

Properties from algebraic geometry.


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



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


  • documentation/latest/fulton/rationaldivisorclassgroup.txt
  • Last modified: 2020/01/22 09:02
  • (external edit)