Equations for $\bar M_{0,n}$

Details Equations for $\bar M_{0,n}$ Equations for $\bar M_{0,n}$

2005-07-05

arxiv.org/abs/math/0507093v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

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 $P^1 \times P^2 \times ... \times P^{n-3}$, permuted by the symmetric group. The homogeneous ideal of $\bar M_{0,n}$ is the sum of the homogeneous ideals of these Segre embeddings.

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