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Generalising Kapranov's theorem for tropical geometry over hyperfields

James Maxwell

Journal of Algebra, Volume: 638, Pages: 441 - 464

Swansea University Author: James Maxwell

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DOI (Published version): 10.1016/j.jalgebra.2023.09.018

Abstract

Kapranov's theorem is a foundational result in tropical geometry. It states that the set of tropicalisations of points on a hypersurface coincides precisely with the tropical variety of the tropicalisation of the defining polynomial.

Published in: Journal of Algebra
ISSN: 0021-8693 1090-266X
Published: Elsevier BV 2024
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa64706
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Abstract: Kapranov's theorem is a foundational result in tropical geometry. It states that the set of tropicalisations of points on a hypersurface coincides precisely with the tropical variety of the tropicalisation of the defining polynomial.
Keywords: Hyperfield, Hyperoperation, Polynomials, Varieties, RAC
College: Faculty of Science and Engineering
Funders: UKRI, EP/R51312X/1
Start Page: 441
End Page: 464

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