standard basis -- The standard basis of symmetric divisors for the moduli space of stable n-pointed genus zero curves

The standard basis of the $Q$-vector space of $S_n$ symmetric divisors on $\bar{M}_{0,n}$ is given by the boundary divisors $B_i$, as we now explain. Let $\Delta_I$ be the closure of the locus of curves with two irreducible components meeting at one node such that the marked points with labels in $I$ lie on the first component, and the marked points with labels in $I^c$ lie on the second component. Then $B_i= \sum_{\#I=i} \Delta_I$, and the divisors $B_2, ..., B_{[n/2]}$ form a basis of the space of symmetric divisors. See [KM].