A comparison of positivity in complex and tropical toric geometry
| Autor: | Philipp Jell, José Ignacio Burgos Gil, Walter Gubler, Klaus Künnemann |
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| Přispěvatelé: | Ministerio de Economía y Competitividad (España), Ministerio de Ciencia e Innovación (España) |
| Rok vydání: | 2021 |
| Předmět: |
ddc:510
Primary 14L32 Secondary 14T05 32U05 32U40 Pure mathematics Mathematics - Number Theory Mathematics - Complex Variables General Mathematics 010102 general mathematics Toric variety 510 Mathematik 01 natural sciences Mathematics - Algebraic Geometry Cone (topology) 0103 physical sciences Lattice theorem FOS: Mathematics Toric varieties · Tropicalization · Positive currents · Lagerberg forms Number Theory (math.NT) 010307 mathematical physics Complex Variables (math.CV) 0101 mathematics Invariant (mathematics) Algebraic Geometry (math.AG) Physics::Atmospheric and Oceanic Physics Mathematics |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname |
| Popis: | 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. Final version, 50 pages, 1 figure, to appear in Mathematische Zeitschrift |
| Databáze: | OpenAIRE |
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