Séminaire Lotharingien de Combinatoire, B47f (2002), 19 pp.
Vincenzo Marra and Daniele Mundici
Combinatorial Fans,
Lattice-ordered Groups, and Their Neighbours: A Short Excursion
Abstract.
Just like the celebrated dictionary between integral convex
geometry and toric varieties bridged until then remote
mathematical worlds, the less well-known duality between (certain)
lattice-ordered groups and rational polyhedral sets brought
combinatorial techniques to bear on the investigation of these
abstract algebraic structures. We offer a brief excursion into
these relatively new territories, with special emphasis on the
novel and admittedly unclear rôle played by order-theoretical
considerations.
Received: March 4, 2002;
Accepted: April 9, 2002.
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