isQQCartier(ToricDivisor) -- whether a torus-invariant Weil divisor is QQ-Cartier

Synopsis

• Function: isQQCartier

• Usage:

  isCartier D

• Inputs:
  • D, a toric divisor,
• Outputs:
  • a Boolean value, that is true if the divisor is $\QQ$-Cartier

Description

i1 : W = weightedProjectiveSpace {2,5,7};

i2 : assert isSimplicial W

i3 : assert not isCartier W_0

i4 : assert isQQCartier W_0

i5 : assert isCartier (35*W_0)

i6 : X = normalToricVariety (id_(ZZ^3) | -id_(ZZ^3));

i7 : assert not isCartier X_0

i8 : assert not isQQCartier X_0

i9 : K = toricDivisor X;

o9 : ToricDivisor on X

i10 : assert isCartier K

See also

• working with divisors -- information about toric divisors and their related groups
• cartierDivisorGroup(NormalToricVariety) -- compute the group of torus-invariant Cartier divisors
• isSimplicial(NormalToricVariety) -- whether a normal toric variety is simplicial
• isCartier(ToricDivisor) -- whether a torus-invariant Weil divisor is Cartier