fromCDivToPic X
The Picard group of a variety is the group of Cartier divisors divided by the subgroup of principal divisors. For a normal toric variety , the Picard group has a presentation defined by the map from the group of torus-characters to the group of torus-invariant Cartier divisors. Hence, there is a surjective map from the group of torus-invariant Cartier divisors to the Picard group. This function returns a matrix representing this map with respect to the chosen bases. For more information, see Theorem 4.2.1 in Cox-Little-Schenck's Toric Varieties.
On a smooth normal toric variety, the map from the torus-invariant Cartier divisors to the Picard group is the same as the map from the Weil divisors to the class group.
|
|
|
|
|
|
|
|
|
|
|
|
In general, there is a commutative diagram relating the map from the group of torus-invariant Cartier divisors to the Picard group and the map from the group of torus-invariant Weil divisors to the class group.
|
|
|
|
|
|
|
|
|
|
|
|
This map is computed and cached when the Picard group is first constructed.