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NormalToricVarieties :: NormalToricVariety _ ZZ

NormalToricVariety _ ZZ -- make a torus-invariant prime divisor

Synopsis

Description

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;
i2 : PP2_0

o2 = D
      0

o2 : ToricDivisor on PP2
i3 : PP2_1

o3 = D
      1

o3 : ToricDivisor on PP2
i4 : PP2_2

o4 = D
      2

o4 : ToricDivisor on PP2
i5 : - PP2_0 - PP2_1 - PP2_2 === toricDivisor PP2 

o5 = true
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));
i7 : X_0

o7 = D
      0

o7 : ToricDivisor on X
i8 : #support X_0

o8 = 1
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
i10 : #support toricDivisor X

o10 = 8

See also