killsCurves -- given an S_n symmetric divisor D, produces a list of symmetric F-curves C such that C dot D = 0

Synopsis

Usage:

killsCurves(D)
Inputs:
- D, an instance of the type SymmetricDivisorM0nbar,
Outputs:
- L, a list,

Description

Given a symmetric divisor D on $\bar{M}_{0,n}$, this function returns the list of symmetric F curves $C$ such that $D . C=0$.

Here is an example from the paper [AGSS]: When n is even, the divisor $D^n_{1,n/2}$ is zero on even F-curves and 1 on odd F-curves. (Here the parity of $F_{a,b,c,d}$ is defined to be the parity of the product $abcd$.) In the calculations below, we check this claim for $n=8$.

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 : killsCurves(D)

o2 = {{4, 2, 1, 1}, {3, 2, 2, 1}, {2, 2, 2, 2}}

o2 : List

Ways to use killsCurves :

killsCurves(SymmetricDivisorM0nbar)

For the programmer

The object killsCurves is a method function.