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Riemann functions, their weights, and modeling Riemann-Roch formulas as Euler characteristics Nicolas, Folinsbee
Abstract
In this thesis, we discuss modelling with (virtual) k-diagrams a class of functions from ℤⁿ to ℤ, which we call Riemann functions, that generalize the graph Riemann-Roch rank functions of Baker and Norine. The graph Riemann-Roch theorem has seen significant activity in recent years, however, as of yet, there is not a satisfactory homological interpretation of this theorem. This may be viewed as disappointing given the rich homological theory contained in the classical Riemann-Roch theorem. For a graph Riemann-Roch function, we will be able to express the associated graph Riemann-Roch formula as a (virtual) Euler characteristic of the modelling (virtual) k-diagram. From the development of this approach, we obtain a new formula for computing the graph Riemann-Roch rank of the complete graph Kn.
Item Metadata
Title |
Riemann functions, their weights, and modeling Riemann-Roch formulas as Euler characteristics
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Creator | |
Supervisor | |
Publisher |
University of British Columbia
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Date Issued |
2022
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Description |
In this thesis, we discuss modelling with (virtual) k-diagrams a class of functions from ℤⁿ to ℤ, which we call Riemann functions, that generalize the graph Riemann-Roch rank functions of Baker and Norine. The graph Riemann-Roch theorem has seen significant activity in recent years, however, as of yet, there is not a satisfactory homological interpretation of this theorem. This may be viewed as disappointing given the rich homological theory contained in the classical Riemann-Roch theorem. For a graph Riemann-Roch function, we will be able to express the associated graph Riemann-Roch formula as a (virtual) Euler characteristic of the modelling (virtual) k-diagram. From the development of this approach, we obtain a new formula for computing the graph Riemann-Roch rank of the complete graph Kn.
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Genre | |
Type | |
Language |
eng
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Date Available |
2022-01-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0406221
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2022-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International