Super currents and tropical geometry
By Aron Lagerberg. 2010
62 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ef2caf193cf1a61d04844fc1eb9f3d375ec186ec
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In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Singular semipositive metrics in non-Archimedean geometry (2011, background): “ion have been taken in [CLD12] (see also [Gub13] for a nice account on these developments), where the notions of positive forms and currents are introduced, partially building upon ideas by Lagerberg [Lag12]. Our approach is geometric, and we restrict our attention to the discretely valued case in o”
- Formes différentielles réelles et courants sur les espaces de Berkovich (2012, unknown): “Dans ce cas, ∫ ∂C 〈ω, ∂µ〉 fait intervenir des (n−1)-faces qui sont intérieures à P .”