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ConformalBlocks :: isSymmetricFDivisor

isSymmetricFDivisor -- checks whether a symmetric divisor intersects all the F-curves nonnegatively

Synopsis

Description

We say a symmetric divisor on $\bar{M}_{0,n}$ is a symmetric F-divisor if $D . F_{I_1,I_2,I_3,I_4} \geq 0$ for every F curve.

In the example below, we see that for $n=8$, the divisor $3B_2+2B_3+4B_4$ is a symmetric F-divisor, while the divisor $B_2$ is not.

i1 : D=symmetricDivisorM0nbar(8,3*B_2+2*B_3+4*B_4)

o1 = 3*B  + 2*B  + 4*B
        2      3      4

o1 : S_8-symmetric divisor on M-0-8-bar
i2 : isSymmetricFDivisor(D)

o2 = true
i3 : D=symmetricDivisorM0nbar(8,B_2)

o3 = B
      2

o3 : S_8-symmetric divisor on M-0-8-bar
i4 : isSymmetricFDivisor(D)
This divisor has negative intersection with the F curve F_{3, 2, 2, 1} (and maybe others too)

o4 = false

Ways to use isSymmetricFDivisor :

For the programmer

The object isSymmetricFDivisor is a method function.