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FCurveDotConformalBlockDivisor -- intersection of an F-curve with a conformal block divisor



This function implements the formulas given in [Fakh] Prop. 2.7 and Cor. 3.5. Note: in contrast with most of the other functions in this package, this function is for UNsymmetrized curves and bundles. The F curve must be entered as a partition of the set {1,...,n} into four nonempty subsets.

The example below shows that the first Chern class of the conformal block bundle $V(sl_2,1,(1,1,1,1,1,1))$ intersects the F curve $F_{123,4,5,6}$ positively, and intersects $F_{12,34,5,6}$ in degree zero.

i1 : sl_2=simpleLieAlgebra("A",1);
i2 : V=conformalBlockVectorBundle(sl_2,1,{{1},{1},{1},{1},{1},{1}},0);
i3 : FCurveDotConformalBlockDivisor({{1,2,3},{4},{5},{6}},V)

o3 = 1
i4 : FCurveDotConformalBlockDivisor({{1,2},{3,4},{5},{6}},V)

o4 = 0
i5 : sl_3=simpleLieAlgebra("A",2);
i6 : W=conformalBlockVectorBundle(sl_3,1,{{0,1},{1,0},{1,0},{1,0},{1,0}},0);
i7 : FCurveDotConformalBlockDivisor({{4,5},{1},{2},{3}},W)

o7 = 1

Ways to use FCurveDotConformalBlockDivisor :

For the programmer

The object FCurveDotConformalBlockDivisor is a method function.