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NormalToricVarieties :: fromPicToCl

fromPicToCl -- get the map from Picard group to class group

Synopsis

Description

The Picard group of a normal toric variety is a subgroup of the class group.

On a smooth normal toric variety, the Picard group is isomorphic to the class group, so the inclusion map is the identity.

PP3 = projectiveSpace 3;
pic PP3
cl PP3
fromPicToCl PP3
FF7 = hirzebruchSurface 7;
pic FF7 == cl FF7
fromPicToCl FF7
For weighted projective space, the inclusion corresponds to l ℤ in , where l = lcm(q0,…, qd ).
X = weightedProjectiveSpace {1,2,3};
pic X
cl X
fromPicToCl X
Y = weightedProjectiveSpace {1,2,2,3,4};
pic Y
cl Y
fromPicToCl Y
The following examples illustrate some other possibilities.
C = normalToricVariety({{1,0,0},{0,1,0},{0,0,1},{1,1,-1}},{{0,1,2,3}});
pic C
cl C
fromPicToCl C
X = normalToricVariety(id_(ZZ^3) | - id_(ZZ^3));
rays X
max X
pic X
cl X
fromPicToCl X
prune cokernel fromPicToCl X

See also

Ways to use fromPicToCl :