====== BigObject RationalDivisorClassGroup ======
//from application [[..:fulton|fulton]]//\\
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 The class group Cl(X) of Weil divisors on the toric variety defined by the fan is a finitely generated abelian group of rank [[..:fan:PolyhedralFan#N_RAYS |N_RAYS]]-[[..:fan:PolyhedralFan#DIM |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 =====

==== Algebraic Geometry ====
 Properties from algebraic geometry.
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{{anchor:lifting:}}
  ?  **''LIFTING''**
  :: Lifts a divisor in the class group onto a divisor on the fan.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<[[..:common#Integer |Integer]],[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:projection:}}
  ?  **''PROJECTION''**
  :: Maps a divisor on the variety onto its representation in the class group.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<[[..:common#Integer |Integer]],[[..:common#NonSymmetric |NonSymmetric]]>''


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