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# ToricDivisor * List -- restriction of a Cartier toric divisor to the orbit closure of a cone

## Synopsis

• Operator: *
• Usage:
D*C
• Inputs:
• Outputs:
• , Returns the toric cycle given by restricting a Cartier toric divisor to the orbit closure of the given cone

## Description

 i1 : rayList={{1,0},{0,1},{-1,-1},{0,-1}} o1 = {{1, 0}, {0, 1}, {-1, -1}, {0, -1}} o1 : List i2 : coneList={{0,1},{1,2},{2,3},{3,0}} o2 = {{0, 1}, {1, 2}, {2, 3}, {3, 0}} o2 : List i3 : X = normalToricVariety(rayList,coneList) o3 = X o3 : NormalToricVariety i4 : D = X_3 o4 = X 3 o4 : ToricDivisor on X

The only cone containing rays 2 and 3 is the cone {2,3}. There is no cone containing rows 1 and 3.

 i5 : D*{2} o5 = X {2, 3} o5 : ToricCycle on X i6 : D*{1} o6 = 0 o6 : ToricCycle on X

This can also compute more complicated sums.

 i7 : D = X_0 + 2*X_1 + 3*X_2 + 4*X_3 o7 = X + 2*X + 3*X + 4*X 0 1 2 3 o7 : ToricDivisor on X i8 : C = (orbits X)#1#0 o8 = {0} o8 : List i9 : D*C o9 = 6*X {0, 3} o9 : ToricCycle on X