A comparison of positivity in complex and tropical toric geometry

Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex tor...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2021-12, Vol.299 (3-4), p.1199-1255
Main Authors: Burgos Gil, José Ignacio, Gubler, Walter, Jell, Philipp, Künnemann, Klaus
Format: Article
Language:English
Subjects:
Harmonic functions
Invariants
Mathematics
Mathematics and Statistics
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Summary:Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford–Taylor theory of plurisubharmonic functions on the tropicalization.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-021-02697-8