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NormalToricVarieties :: isQQCartier

isQQCartier -- whether a torus-invariant Weil divisor is QQ-Cartier

Synopsis

Description

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

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

i1 : W = weightedProjectiveSpace {2,5,7};
i2 : isSimplicial W

o2 = true
i3 : isCartier W_0    

o3 = false
i4 : isQQCartier W_0

o4 = true
i5 : isCartier (35*W_0)      

o5 = true
In general, the -Cartier divisors form a proper subgroup of the Weil divisors.
i6 : X = normalToricVariety(id_(ZZ^3) | -id_(ZZ^3));
i7 : isCartier X_0

o7 = false
i8 : isQQCartier X_0

o8 = false
i9 : K = toricDivisor X

o9 = - D  - D  - D  - D  - D  - D  - D  - D
        0    1    2    3    4    5    6    7

o9 : ToricDivisor on X
i10 : isCartier K

o10 = true

See also

Ways to use isQQCartier :