2013/11/07 by Di Rocco, Sandra
#14M25 #14N30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1311.1625
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory.