A Weil divisor is
ℚ-Cartier if some positive integer multiple is Cartier.
On a simplicial toric variety, every torus-invariant Weil divisor is
ℚ-Cartier.
i1 : W = weightedProjectiveSpace {2,5,7};
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i2 : isSimplicial W
o2 = true
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i3 : isCartier W_0
o3 = false
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i4 : isQQCartier W_0
o4 = true
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i5 : isCartier (35*W_0)
o5 = true
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In general, the
ℚ-Cartier divisors form a proper subgroup of the Weil divisors.
i6 : X = normalToricVariety(id_(ZZ^3) | -id_(ZZ^3));
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i7 : isCartier X_0
o7 = false
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i8 : isQQCartier X_0
o8 = false
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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
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i10 : isCartier K
o10 = true
|