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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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first_indexed 2023-10-13T14:13:53Z
last_indexed 2023-10-13T14:13:53Z
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spelling v2 64706 2023-10-11 Generalising Kapranov's theorem for tropical geometry over hyperfields 8ad09d7f02687755ec30c7bb4c99c9ac James Maxwell James Maxwell true false 2023-10-11 SMA 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. Journal Article Journal of Algebra 638 441 464 Elsevier BV 0021-8693 1090-266X Hyperfield, Hyperoperation, Polynomials, Varieties, RAC 15 1 2024 2024-01-15 10.1016/j.jalgebra.2023.09.018 http://dx.doi.org/10.1016/j.jalgebra.2023.09.018 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University SU Library paid the OA fee (TA Institutional Deal) UKRI, EP/R51312X/1 2023-11-08T12:25:21.5068912 2023-10-11T09:07:25.1145430 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics James Maxwell 1 64706__28972__4b7043f4bd274aedbddb3a25592ba6a7.pdf 64706.VOR.pdf 2023-11-08T12:23:49.3948314 Output 460994 application/pdf Version of Record true © 2023 The Author(s). Published by Elsevier Inc. Distributed under the terms of a Creative Commons Attribution 4.0 International License (CC BY 4.0). true eng https://creativecommons.org/licenses/by/4.0/
title Generalising Kapranov's theorem for tropical geometry over hyperfields
spellingShingle Generalising Kapranov's theorem for tropical geometry over hyperfields
James Maxwell
title_short Generalising Kapranov's theorem for tropical geometry over hyperfields
title_full Generalising Kapranov's theorem for tropical geometry over hyperfields
title_fullStr Generalising Kapranov's theorem for tropical geometry over hyperfields
title_full_unstemmed Generalising Kapranov's theorem for tropical geometry over hyperfields
title_sort Generalising Kapranov's theorem for tropical geometry over hyperfields
author_id_str_mv 8ad09d7f02687755ec30c7bb4c99c9ac
author_id_fullname_str_mv 8ad09d7f02687755ec30c7bb4c99c9ac_***_James Maxwell
author James Maxwell
author2 James Maxwell
format Journal article
container_title Journal of Algebra
container_volume 638
container_start_page 441
publishDate 2024
institution Swansea University
issn 0021-8693
1090-266X
doi_str_mv 10.1016/j.jalgebra.2023.09.018
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1016/j.jalgebra.2023.09.018
document_store_str 1
active_str 0
description 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_date 2024-01-15T12:25:25Z
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score 11.016503

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