Lecture by Frank Sottile (Texas University): Irrational toric varieties and the secondary polytope

Jan 06, 2020 | 02:15 PM

The secondary fan of a point configuration A in R^n encodes all regular subdivisions of A. These subdivisions also record all limiting objects obtained by weight degenerations of the irrational toric variety X_A parameterized by A. The secondary fan is the normal fan of the secondary polytope. We explain a functorial construction of R^n-equivariant cell complexes from fans that, when applied to the secondary fan, realizes the secondary polytope as the moduli space of translations and degenerations of X_A. This extends the work of Kapranov, Sturmfels and Zelevinsky (who established this for complex toric varieties when A is integral) to all real configurations A.

Time & Location

Jan 06, 2020 | 02:15 PM

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
Room 005 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)