The torus-invariant prime divisors on a normal toric variety correspond to the rays in the associated fan. In this package, the rays are ordered and indexed by the nonnegative integers. Given a normal toric variety and nonnegative integer, this method returns the corresponding torus-invariant prime divisor. The most convenient way to make a general torus-invariant Weil divisor is to simply write the appropriate linear combination of these torus-invariant Weil divisors.
There are three torus-invariant prime divisors in the projective plane.
i1 : PP2 = projectiveSpace 2;
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i2 : PP2_0
o2 = D
0
o2 : ToricDivisor on PP2
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i3 : PP2_1
o3 = D
1
o3 : ToricDivisor on PP2
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i4 : PP2_2
o4 = D
2
o4 : ToricDivisor on PP2
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i5 : - PP2_0 - PP2_1 - PP2_2 === toricDivisor PP2
o5 = true
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A torus-invariant Weil divisor is prime if and only if its support has a single element.
i6 : X = normalToricVariety(id_(ZZ^3) | -id_(ZZ^3));
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i7 : X_0
o7 = D
0
o7 : ToricDivisor on X
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i8 : #support X_0
o8 = 1
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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 : #support toricDivisor X
o10 = 8
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