Degenerations for products of psi and omega classes on M_{0,n}-bar

I'll give an introduction to the moduli space M_{0,n}-bar of n-marked genus zero stable curves, emphasizing concrete aspects of its geometry as a variety: boundary strata, coordinates, and how to calculate degenerations with it.

I will describe recent joint work with Maria Gillespie and Sean Griffin, on products of psi and omega classes on the moduli space of stable curves of genus zero.

We construct a flat family of subschemes of M_{0,n}-bar, whose general fiber is a complete intersection representing the product, and whose special fiber is a generically reduced union of boundary strata. Our family uses an explicit set of parametrized hyperplane equations, and the resulting strata are enumerated by a combinatorial rule we call "slide labeling" on trees.

As such, we express these products as positive, multiplicity-free sums of boundary classes in the Chow ring. As a corollary, we also express the kappa classes as positive sums of boundary classes.