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Higher rank tropicalization / XUAN GAO

Swansea University Author: XUAN GAO

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DOI (Published version): 10.23889/SUThesis.67181

Abstract

A higher rank valuation is a function that maps a field to the union of an ordered abelian group and infinity. There are studies that have shown that Kapranov’s theorem still holds when the valuation is of rank n > 1 and the rank n tropicalization of a d-dimensional variety is a polyhedral complex...

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Published: Swansea University, Wales, UK 2024
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: Giansiracusa, J., & Beggs, E. J.
URI: https://cronfa.swan.ac.uk/Record/cronfa67181
first_indexed 2024-07-25T10:52:14Z
last_indexed 2024-11-25T14:19:40Z
id cronfa67181
recordtype RisThesis
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spelling 2024-07-25T11:56:22.4220557 v2 67181 2024-07-25 Higher rank tropicalization 62271f259d8f2044f63a2745b4dbf920 XUAN GAO XUAN GAO true false 2024-07-25 A higher rank valuation is a function that maps a field to the union of an ordered abelian group and infinity. There are studies that have shown that Kapranov’s theorem still holds when the valuation is of rank n > 1 and the rank n tropicalization of a d-dimensional variety is a polyhedral complex of dimension nd, etc. This thesis aims to focus on higher rank valuation, we present a method about how to reduce a higher rank valuation to a sequence of classic valuations. With this method, we can describe the structure of the tropicalization over a higher rank valuation in terms of rank 1 tropicalisations, which will help us to reprove Kapranov’s theorem in an alternative way. E-Thesis Swansea University, Wales, UK Tropical Geometry 25 6 2024 2024-06-25 10.23889/SUThesis.67181 A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. COLLEGE NANME COLLEGE CODE Swansea University Giansiracusa, J., & Beggs, E. J. Doctoral Ph.D 2024-07-25T11:56:22.4220557 2024-07-25T11:43:37.7433466 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science XUAN GAO 1 67181__30976__11580b1967e141e29638ab5bc6cb1d6d.pdf 2024_Gao_X.final.67181.pdf 2024-07-25T11:51:19.1760502 Output 636821 application/pdf E-Thesis – open access true Copyright: The Author, Xuan Gao, 2024 Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0) true eng https://creativecommons.org/licenses/by/4.0/
title Higher rank tropicalization
spellingShingle Higher rank tropicalization
XUAN GAO
title_short Higher rank tropicalization
title_full Higher rank tropicalization
title_fullStr Higher rank tropicalization
title_full_unstemmed Higher rank tropicalization
title_sort Higher rank tropicalization
author_id_str_mv 62271f259d8f2044f63a2745b4dbf920
author_id_fullname_str_mv 62271f259d8f2044f63a2745b4dbf920_***_XUAN GAO
author XUAN GAO
author2 XUAN GAO
format E-Thesis
publishDate 2024
institution Swansea University
doi_str_mv 10.23889/SUThesis.67181
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 - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description A higher rank valuation is a function that maps a field to the union of an ordered abelian group and infinity. There are studies that have shown that Kapranov’s theorem still holds when the valuation is of rank n > 1 and the rank n tropicalization of a d-dimensional variety is a polyhedral complex of dimension nd, etc. This thesis aims to focus on higher rank valuation, we present a method about how to reduce a higher rank valuation to a sequence of classic valuations. With this method, we can describe the structure of the tropicalization over a higher rank valuation in terms of rank 1 tropicalisations, which will help us to reprove Kapranov’s theorem in an alternative way.
published_date 2024-06-25T12:38:41Z
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score 10.905303

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