Computational Algebra Seminar: Pfaffenholz -- Polyhedral Adjunction Theory

Speaker: Andreas Pfaffenholz (TU Darmstadt)
Title: Polyhedral Adjunction Theory
Time & Place: 3:05-4pm, Thursday 15 November, Carslaw 535

Abstract: 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 $\mu$ and the nef-value
$\tau$ of a polarized toric variety associated to a lattice polytope. The
polyhedral description allows explicit computations e.g.\ with the software
\texttt{polymake}. As a main result I will show that a $d$-dimensional
lattice polytope $P$ has lattice width one if $\mu\ge (d+2)/2$ and give
some combinatorial and algebraic implications.

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