University of Minnesota Combinatorics Seminar: 2020-2021

Date: 10/23/2020

Speaker: John Machacek

Posets, Cones, and Toric Varieties
To any poset on [n] we can associate a cone in a natural way. This is done by a correspondence between $i < j$ and the half-space $x_i \leq x_j$. To any cone (or fan of cones) we have a toric variety. We consider translations back and forth between properties of posets and toric varieties. From this point of view we can establish Oda's strong factorization conjecture in the special case of fans arising from posets. We will also preview in progress work joint with Josh Hallam on crepant resolutions and the Gorenstein property for toric varieties associated to posets.

Posets, Cones, and Toric Varieties

To any poset on [n] we can associate a cone in a natural way. This is done by a correspondence between $i < j$ and the half-space $x_i \leq x_j$. To any cone (or fan of cones) we have a toric variety. We consider translations back and forth between properties of posets and toric varieties. From this point of view we can establish Oda's strong factorization conjecture in the special case of fans arising from posets. We will also preview in progress work joint with Josh Hallam on crepant resolutions and the Gorenstein property for toric varieties associated to posets.