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NormalToricVarieties :: toricDivisor(List,NormalToricVariety)

toricDivisor(List,NormalToricVariety) -- make a torus-invariant Weil divisor

Synopsis

Description

Given a list of integers and a normal toric variety, this method returns the torus-invariant Weil divisor such the coefficient of the i-th irreducible torus-invariant divisor is the i-th entry in the list. The indexing of the irreducible torus-invariant divisors is inherited from the indexing of the rays in the associated fan. In this package, the rays are ordered and indexed by the nonnegative integers.

i1 : PP2 = toricProjectiveSpace 2;
i2 : D = toricDivisor({2,-7,3},PP2)

o2 = 2*PP2  - 7*PP2  + 3*PP2
          0        1        2

o2 : ToricDivisor on normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} )))))
i3 : assert(D == 2* PP2_0 - 7*PP2_1 + 3*PP2_2)
i4 : assert(D == toricDivisor(entries D, variety D))

Although this is a general method for making a torus-invariant Weil divisor, it is typically more convenient to simple enter the appropriate linear combination of torus-invariant Weil divisors.

See also