Back to Algebraic Geometry Seminar: Spring 2009
Algebraic Geometry Seminar
Date: Tuesday, Feb 10, 2009
Time: 3:30PM - 4:30PM
Location: LCB 215
Ana-Maria Castravet
University of Arizona
Title |
Exceptional loci on moduli spaces of rational n-pointed curves |
Abstract |
The Grothendieck-Knudsen moduli space of stable, n-pointed rational curves is a fascinating variety whose geometry is still little understood. In particular, one would like to understand its effective cones (of curves or of divisors), its birational modifications, etc. A natural question is if boundary strata generate these cones. This is false for divisors by an example of Keel and Vermeire (for n=6) and still unknown for curves (this is known as the Fulton Conjecture). In some joint work with Jenia Tevelev, we identify the interior of the moduli space with a Brill-Noether locus of various very special reducible curves associated to hypergraphs. This allows us to construct factorially many new extremal (non-boundary) divisors of the effective cone, as well as some rigid curves and morphisms with small exceptional locus. |
Algebraic Geometry