Super currents and tropical geometry

2010/08/17 by Aron Lagerberg, Lagerberg, Aron · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1008.2856

openalex publication_date 2010/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the formalism of positive super currents on ℝⁿ, in strong analogy with the theory of positive currents in ℂⁿ. We consider intersection of currents and Lelong numbers, and as an application we show that the formalism can be used to describe tropical varieties. This is similar in spirit to the fact that in complex analysis the current of integration of an analytic variety can be identified with a closed, positive current.

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