Type: Seminar

Distribution: World

Expiry: 15 Nov 2012

Auth: billu@daumier.maths.usyd.edu.au

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).