A Field of Generalised Puiseux Series for Tropical Geometry

Abstract

In this paper we define a field K of characteristic zero with valuation whose value group is the real numbers, and we show that this field of generalised Puiseux series is algebraically closed and complete with respect to the norm induced by its valuation. We consider this field to be a good candidate for the base field for tropical geometry.

References in corpus (4)

• Tropical Geometry and its applications
• The j-invariant of a plane tropical cubic
• An algorithm for lifting points in a tropical variety
• A tropical approach to secant dimensions

Cited by in corpus (16)

• Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
• Log-barrier interior point methods are not strongly polynomial
• Tropicalizing the simplex algorithm
• Tropical types and associated cellular resolutions
• Tropical curves with a singularity in a fixed point
• Algebraic solution of tropical polynomial optimization problems
• Standard Bases in mixed Power Series and Polynomial Rings over Rings
• Tropical approach to Nagata's conjecture in positive characteristic
• Tropical totally positive matrices
• Algebraic solution of tropical best approximation problems
• From Polygons to Ultradiscrete Painlevé Equations
• The Newton polygon of a planar singular curve and its subdivision
• Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves
• Asymmetric tropical distances and power diagrams
• On complete classes of valuated matroids
• The tropical discriminant of a polynomial map on a plane