Tropical Geometry

Abstract

Tropical Geometry can be considered as an algebraic geometry over the semifield $ ({\mathbb R}, \max, +) $. The name was coined by French computer scientists to honor the pioneering work of their Brazilian colleague Imre Simon on the max-plus semiring. Alternatively, Tropical Geometry can be understood as the geometry resulting from complex geometry by a certain degeneration process: complex toric varieties are replaced by real linear spaces and, more generally, complex algebraic varieties are replaced by polyhedral complexes, i.e., by piecewise-linear objects.