cartierIndex -- the Cartier index of a Weil divisor

Usage:

N = cartierIndex(L,F)
Inputs:
- L, a list
- F, an instance of the type Fan, a pure and full dimensional fan
Outputs:
- N, an integer

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 = F

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

Caveat

The ordering of the list L must correspond to the ordering of the rays of the fan output by raySortOfFan.

Ways to use cartierIndex:

cartierIndex(List,Fan)

For the programmer

The object cartierIndex is a method function.

The source of this document is in ToricVectorBundles.m2:2473:0.

cartierIndex -- the Cartier index of a Weil divisor

Description

Caveat

See also

Ways to use cartierIndex:

For the programmer