Back to Algebraic Geometry Seminar: Spring 2010
Algebraic Geometry Seminar
Date: Tuesday, Apr 6, 2010
Time: 3:30PM - 4:30PM
Location: LCB 215
Dustin Cartwright
University of California, Berkeley
Title |
Mustafin Varieties |
Abstract |
A Mustafin variety is a degeneration of projective space induced by a point configuration in a Bruhat-Tits building. The special fiber is reduced and Cohen-Macaulay, and its irreducible components form interesting combinatorial patterns. For configurations that lie in one apartment, these patterns are regular mixed subdivisions of scaled simplices, and the Mustafin variety is a twisted Veronese variety built from such a subdivision. This connects our study to tropical and toric geometry. For general configurations, the irreducible components of the special fiber are rational varieties, and any blow-up of projective space along a linear subspace arrangement can arise. A detailed study of Mustafin varieties is undertaken for configurations in the Bruhat-Tits tree of PGL(2) and in the two-dimensional building of PGL(3). The latter yields the classification of Mustafin triangles into 38 combinatorial types. |
Algebraic Geometry