next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
ConformalBlocks :: F curve

F curve -- F curves in the moduli space of stable n-pointed genus zero curves

Let P=P0,P1,P2,P3 be a partition of {1,...,n} into four nonempty subsets. Fix four (arithmetic) genus zero at worst nodal curves Cj for j=0,1,2,3, and #(Pj) marked points on each curve. We call the curves Cj the tails. Mark one additional point xj on each tail. Next, consider 1 with four marked points, y0,...,y3; we call this the spine. Glue the four tails to the spine by identifying xj and yj. Then, as the cross ratio of y0,...,y3 varies, we sweep out a curve FP in M0,n.

The homology class of FP only depends on the partition P, and not on the choice of the tails Cj or the choices of marked points. The classes of the F-curves span H2(M0,n,Q).

If we only consider F-curves up to Sn symmetry, then it is enough to keep track of the four integers #(P0), #(P1), #(P2), #(P3).