The group of torus-invariant Weil divisors on a normal toric variety is the free abelian group generated by the torus-invariant prime divisors. The prime divisors correspond to rays in the associated fan. Since the rays are indexed in this package by
0, ..., n, the group of torus-invariant Weil divisors is canonically isomorphic to
ℤn+1.
The examples illustrate various possible Weil groups.
i1 : PP2 = projectiveSpace 2;
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i2 : #rays PP2
o2 = 3
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i3 : wDiv PP2
3
o3 = ZZ
o3 : ZZ-module, free
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i4 : FF7 = hirzebruchSurface 7;
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i5 : #rays FF7
o5 = 4
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i6 : wDiv FF7
4
o6 = ZZ
o6 : ZZ-module, free
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i7 : U = normalToricVariety({{4,-1},{0,1}},{{0,1}});
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i8 : #rays U
o8 = 2
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i9 : wDiv U
2
o9 = ZZ
o9 : ZZ-module, free
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