Equations for ${\bar{M}}_{0,n}$

We show that the log canonical bundle, $\kappa$, of ${\bar{M}}_{0,n}$ is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of $P^1\times P^2\times \mathrm{.}\mathrm{.}\mathrm{.}\times P^{n-3}$, permuted by the symmetric group. The homogeneous ideal of ${\bar{M}}_{0,n}$ is the sum of the homogeneous ideals of these Segre embeddings.