Discriminants, Polytopes, and Toric Geometry

Abstract

AbstractToric varieties can be considered as a meeting point of algebra, geometry, and combinatorics. Though they constitute only a small subset of all algebraic varieties, their structure is rich enough to make them interesting when formulating and testing conjectures. Because of their combinatorial description, results in algebraic geometry can sometimes be proved using combinatorics, and combinatorial results can sometimes be proved by algebraic-geometric methods. In this note we will survey results by several authors concerning the description of dual and higher-order dual varieties of toric varieties in terms of their associated lattice polytopes. Toric varieties that are ruled correspond to Cayley polytopes, and we will describe several properties and characterizations of Cayley polytopes using toric geometry.KeywordsLine BundleProjective VarietyToric VarietyChern ClassDual VarietyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.