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SUMMARY:Moduli of stable rational curves and nonlinearizable actions.
DTSTART:20130306T141500
DTEND:20130306T160000
DTSTAMP:20260921T115812Z
UID:cbdce1781daedd71a839621612ce17abc85b9f4f7a30b6a0eab6e276
CATEGORIES:Conferences - Seminars
DESCRIPTION:Brent Doran\, ETHZ\nThe moduli space of stable marked rational
  curves\, M_{0\,n}\, is the subject of intense study\, topologically\, geo
 metrically\, and motivically.  Although recent topological and motivic re
 sults (especially via the period formalism) are quite powerful\, the geome
 tric ones have instead revealed how little is known about its global geome
 try. By replacing the universal torsor with a better homotopy-equivalent m
 odel that more closely encodes the global geometry\, we construct an "alge
 braic uniformization" of M_{0\,n}: it is a geometric invariant theory quot
 ient of affine space by a non-linearizable solvable group action\, providi
 ng a clean algebro-geometric dictionary in the classical sense. Indeed\, i
 t 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.
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STATUS:CONFIRMED
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