next | previous | forward | backward | up | top | index | toc | Macaulay2 website
NormalToricVarieties :: isQQCartier(ToricDivisor)

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



A Weil divisor is $\QQ$-Cartier if some positive integer multiple is Cartier.

On a simplicial toric variety, every torus-invariant Weil divisor is $\QQ$-Cartier.

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)

In general, the $\QQ$-Cartier divisors form a proper subgroup of the Weil divisors.

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