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E-Thesis 643 views 41 downloads

Higher rank tropicalization / XUAN GAO

Swansea University Author: XUAN GAO

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    Copyright: The Author, Xuan Gao, 2024 Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0)

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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
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 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.
Item Description: A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information.
Keywords: Tropical Geometry
College: Faculty of Science and Engineering