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Mustafin Varieties September 19, 2012 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Bernd Sturmfels (University of California, Berkeley; Max-Planck-Institut für Mathematik in den Naturwissenschaften)
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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 components form beautiful combinatorial patterns. For configurations in one apartment, these patterns are mixed subdivisions of simplices, and there is a tight connection to tropical convexity. In general, the components of the special fiber are rational varieties, and any blow-up of projective space along a linear subspace arrangement can arise.
We present a study of the two-dimensional building for PGL(3), joint with Dustin Cartwright, Mathias Haebich and Annette Werner, that classifies Mustafin triangles into 38 combinatorial types.

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