Super currents and tropical geometry

TL;DR

This paper develops a formalism of positive super currents on real space, analogous to complex currents, and applies it to describe tropical varieties, bridging concepts from complex analysis and tropical geometry.

Contribution

It introduces positive super currents on ^n and demonstrates their use in characterizing tropical varieties, a novel approach in tropical geometry.

Findings

Established a theory of positive super currents on ^n.

Connected super currents with tropical varieties.

Provided tools for intersection theory and Lelong numbers in this setting.

Abstract

We introduce the formalism of positive super currents on \mathbb{R}^{n}, in strong analogy with the theory of positive currents in \mathbb{C}^{n}. 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.