E-Thesis 864 views 199 downloads
Higher rank tropicalization / XUAN GAO
Swansea University Author: XUAN GAO
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PDF | E-Thesis – open access
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...
| Published: |
Swansea University, Wales, UK
2024
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| 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. |
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| 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 |