Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: The nef cone of a Coxeter complex: Φ-submodular functions and deformations of Φ-permutahedra

Seminar | March 5 | 3:45-4:45 p.m. | 939 Evans Hall

 Federico Ardila, San Francisco State University

 Department of Mathematics

We describe the nef cone of the toric variety corresponding to a Coxeter complex. Equivalently, this is the cone of deformations of a Coxeter permutahedron. This family contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra and submodular functions to any finite reflection group. This is joint work with Federico Castillo, Chris Eur, and Alex Postnikov.