LINEAR GALE TRANSFORMS AND GELFAND-KAPRANOV-ZELEVINSKIJ DECOMPOSITIONS

Dedicated to Professor Heisuke Hironaka on his sixtieth birthday

Abstract

In the convex-geometric setting of what we call linear Gale transforms and convex polyhedral cone decompositions, we generalize and reformulate results on (1) the secondary polytope of a convex polytope considered by Gelfand, Kapranov and Zelevinskij in connection with the discriminants of projective toric varieties, as well as (2) the wall geometry of fans considered by Reid in connection with Mori's birational geometry in the particular case of projective toric varieties.