The moduli space \( M \)\( _{0,n} \)bar describes nmarked stable curves of genus zero. It has a closed embedding into a product of projective spaces \( P^1 \times\cdots\times P^{n3} \), due to KeelTevelev and Kapranov and involving the tautological "psi" and "omega" divisor classes. Composing this map with the Segre map gives the socalled "log canonical" embedding of \( M \)\( _{0,n} \)bar. Essentially, these maps are the most natural ways to realize \( M \)\( _{0,n} \)bar as a (multi)projective variety.
I will introduce \( M \)\( _{0,n} \)bar and discuss some combinatorics and algebra arising from this embedding. Most notably, Monin and Rana (2017) conjectured a set of equations defining the embedded image of \( M \)\( _{0,n} \)bar in \( P^1 \times \cdots \times P^{n3} \), given by 2by2 minors of certain 2byk matrices, resembling the wellknown equations for Veronese, Segre and Plücker embeddings. We prove this conjecture for all n.
This is joint work with Maria Gillespie and Sean T. Griffin.
