Polyhedral adjunction theory allows to study questions of classical adjunction theory for toric varieties from a purely combinatorial viewpoint. In my talk I will present the convex-geometric invariants corresponding to the (unnormalized) spectral value μ and the nef-value τ of a polarized toric variety associated to a lattice polytope. The polyhedral description allows explicit computations e.g. with the software polymake. As a main result I will show that a d-dimensional lattice polytope P has lattice width one if μ ≥ (d + 2)/2 and give some combinatorial and algebraic implications.

This is joint work with Benjamin Nill, Christian Haase, and Sandra Di Rocco (arxiv:1105.2415).