Moduli of stable rational curves and nonlinearizable actions.
Event details
| Date | 06.03.2013 |
| Hour | 14:15 › 16:00 |
| Speaker | Brent Doran, ETHZ |
| Location | |
| Category | Conferences - Seminars |
The moduli space of stable marked rational curves, M_{0,n}, is the subject of intense study, topologically, geometrically, and motivically. Although recent topological and motivic results (especially via the period formalism) are quite powerful, the geometric ones have instead revealed how little is known about its global geometry. By replacing the universal torsor with a better homotopy-equivalent model that more closely encodes the global geometry, we construct an "algebraic uniformization" of M_{0,n}: it is a geometric invariant theory quotient of affine space by a non-linearizable solvable group action, providing a clean algebro-geometric dictionary in the classical sense. Indeed, it is "one G_a away" from being a toric variety: it follows that, for any given n, any geometric quantity is in principle determined by an explicit combination of topological and invariant-theoretic techniques. The result holds over Spec Z. Joint work with N. Giansiracusa.
Practical information
- General public
- Free