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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