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NormalToricVarieties :: wDiv

wDiv -- make the group of torus-invariant Weil divisors

Synopsis

Description

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 n+1.

The examples illustrate various possible Weil groups.

i1 : PP2 = projectiveSpace 2;
i2 : #rays PP2

o2 = 3
i3 : wDiv PP2

       3
o3 = ZZ

o3 : ZZ-module, free
i4 : FF7 = hirzebruchSurface 7;
i5 : #rays FF7

o5 = 4
i6 : wDiv FF7

       4
o6 = ZZ

o6 : ZZ-module, free
i7 : U = normalToricVariety({{4,-1},{0,1}},{{0,1}});
i8 : #rays U

o8 = 2
i9 : wDiv U

       2
o9 = ZZ

o9 : ZZ-module, free

See also

Ways to use wDiv :