Séminaire de Mathématique

Topology and combinatorics of Toric arrangements

par Prof. Emanuele DELUCCHI (Universität Bremen)

Europe/Paris
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
Description

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.
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