The birational geometry of the moduli space of stable, n-pointed, rational curves is still largely unknown. For example, it is not known if the cone of effective divisors is polyhedral, if the cone of effective curves is generated by 1-strata (Fultons conjecture), or if it has only finitely many small modifications. In a joint work with Jenia Tevelev, we find that some of this complexity can be explained by the fact that this moduli space can be interpreted as the Brill-Noether locus of some very special reducible curves related to hypergraphs. Using this we construct many new extremal divisors and birational morphisms with unexpected exceptional loci.
Combinatorial Algebraic Geometry
Friday, May 9, 2008 - 11:00am
Ana-Maria Castravet
University of Arizona