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ConformalBlocks :: isSymmetricFDivisor

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

Synopsis

Usage:

isSymmetricFDivisor(D)
Inputs:
- D, an instance of the type SymmetricDivisorM0nbar
Outputs:
- b, a Boolean value

Description

We say a symmetric divisor on M_0,n is a symmetric F-divisor if D . F_{I₁,I₂,I₃,I₄} ≥0 for every F curve.

In the example below, we see that for n=8, the divisor 3B₂+2B₃+4B₄ is a symmetric F-divisor, while the divisor B₂ 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` :

isSymmetricFDivisor(SymmetricDivisorM0nbar)