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OldToricVectorBundles :: cartierIndex

cartierIndex -- the Cartier index of a Weil divisor

Synopsis

Description

L must be a list of weights, exactly one for each ray of the fan. Then the Cartier index is the smallest strictly positive natural number $N$ such that $N$ times the Weil divisor is Cartier. If the Weil divisor defined by these weights is not QQ-Cartier, then $N$ would be infinity. In this case cartierIndex returns an error. Otherwise it returns $N$.

i1 : F = fan posHull matrix {{1,5},{5,1}}

o1 = {ambient dimension => 2         }
      number of generating cones => 1
      number of rays => 2
      top dimension of the cones => 2

o1 : Fan
i2 : L = {2,2}

o2 = {2, 2}

o2 : List
i3 : cartierIndex(L,F)

o3 = 3

If we change the Weil divisor we get a different Cartier index:

i4 : L = {3,3}

o4 = {3, 3}

o4 : List
i5 : cartierIndex(L,F)

o5 = 2

See also

Ways to use cartierIndex :

For the programmer

The object cartierIndex is a method function.