Séminaire de Mathématique

Topology and combinatorics of Toric arrangements

by Prof. Emanuele DELUCCHI (Universität Bremen)

Amphitéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

Amphitéâtre Léon Motchane

Institut des Hautes Etudes Scientifiques

Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

A toric arrangement is given by a family A of level sets of characters of a complex torus T. The focus of this talk will be on the topology of the complement M:=T \ A, and in particular on the extent to which M is determined by the combinatorial data of the arrangement A, a line of research recently revived by work of De Concini and Procesi. 
I will first present some basics about toric arrangements, and then hint at how a theoretical framework can be developed in parallel to the theory of hyperplane arrangements. In particular, I will describe combinatorial models for the homotopy type of M and explain the methods we use in our proof of minimality, and thus of torsion-freeness, of M.
This is mostly joint work with Giacomo d'Antonio.