BigObject TDivisor [polymake wiki]

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====== BigObject TDivisor ======
//from application [[..:fulton|fulton]]//\\
\\
 A //T//-invariant divisor on a normal toric variety.

===== Properties =====

==== Algebraic Geometry ====
 Properties from algebraic geometry.
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{{anchor:ample:}}
  ?  **''AMPLE''**
  :: True if the divisor is __ample__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:basepoint_free:}}
  ?  **''BASEPOINT_FREE''**
  :: True if the divisor is __basepoint-free__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:cartier:}}
  ?  **''CARTIER''**
  :: True if the divisor is __Cartier__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:effective:}}
  ?  **''EFFECTIVE''**
  :: True if the divisor is __effective__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:integral:}}
  ?  **''INTEGRAL''**
  :: True if the divisor is __integral__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:nef:}}
  ?  **''NEF''**
  :: True if the divisor is __nef__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:principal:}}
  ?  **''PRINCIPAL''**
  :: True if the divisor is __principal__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:q_cartier:}}
  ?  **''Q_CARTIER''**
  :: A divisor is __Q-Cartier__ if some multiple of it is ''[[..:fulton:TDivisor#CARTIER |CARTIER]]''.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:semiample:}}
  ?  **''SEMIAMPLE''**
  :: True if the divisor is __semiample__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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{{anchor:very_ample:}}
  ?  **''VERY_AMPLE''**
  :: True if the divisor is __very ample__.
    ? Type:
    :''[[..:common#Bool |Bool]]''


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==== Combinatorics ====
 These properties capture combinatorial information of the object.  Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.
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{{anchor:cartier_data:}}
  ?  **''CARTIER_DATA''**
  :: Contains the __Cartier data__ of the divisor if it is ''[[..:fulton:TDivisor#CARTIER |CARTIER]]'', i.e., contains a list of vertices of the lattice polytope defined by the divisor and the variety. The vertices appear in the same order as the maximal cones of the fan.
    ? Type:
    :''[[..:common#Map |Map]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]>,[[..:common#Vector |Vector]]<[[..:common#Rational |Rational]]%%>>%%''


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{{anchor:coefficients:}}
  ?  **''COEFFICIENTS''**
  :: The divisor on a toric variety, given as a list of coefficients for the torus invariant divisors corresponding to the [[..:fan:PolyhedralFan#RAYS |RAYS]] of the fan. Take care of labeling of the Rays.
    ? Type:
    :''[[..:common#Vector |Vector]]<[[..:common#Rational |Rational]]>''


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{{anchor:section_polytope:}}
  ?  **''SECTION_POLYTOPE''**
  :: The polytope whose lattice points correspond to the global sections of the divisor.
    ? Type:
    :''[[..:polytope:Polytope |Polytope]]<[[..:common#Rational |Rational]]>''


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