A comparison of positivity in complex and tropical toric geometry

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 08 Mar 2021Embargo end date: 01 Jan 2020 English Publisher:Springer Science and Business Media LLCJournal:Mathematische Zeitschrift, volume 299, pages 1,199-1,255 (issn: 0025-5874, eissn: 1432-1823,

Copyright policy )Funded by:DFG | Higher Invariants – Inter...

Authors: José Ignacio Burgos Gil; Walter Gubler; Philipp Jell; Klaus Künnemann;

doi: 10.1007/s00209-021-02697-8 , 10.5283/epub.52554 , 10.48550/arxiv.2003.08644

arXiv: 2003.08644

handle: 10261/253298

A comparison of positivity in complex and tropical toric geometry

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Abstract

AbstractGiven 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.

Related Organizations

Spanish National Research Council
Spain
Autonomous University of Madrid
Spain
Institute of Mathematical Sciences
Spain
University of Regensburg
Germany

Keywords

Research exposition (monographs, survey articles) pertaining to algebraic geometry, Lagerberg forms, Mathematics - Algebraic Geometry, Currents, FOS: Mathematics, Number Theory (math.NT), Arithmetic varieties and schemes; Arakelov theory; heights, Complex Variables (math.CV), Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic Geometry (math.AG), Toric varieties; Tropicalization; Positive currents; Lagerberg forms, Primary 14L32, Secondary 14T05, 32U05, 32U40, tropicalization, Mathematics - Number Theory, Arithmetic aspects of tropical varieties, Mathematics - Complex Variables, 510 Mathematik, Rigid analytic geometry, Foundations of tropical geometry and relations with algebra, positive currents, Plurisubharmonic functions and generalizations, toric varieties

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