 [2406.03987] Clifford representatives via the uniform algebraic rank




























  








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Mathematics > Algebraic Geometry


arXiv:2406.03987 (math)
    




  [Submitted on 6 Jun 2024]
Title:Clifford representatives via the uniform algebraic rank
Authors:Myrla Barbosa, Karl Christ, Margarida Melo View a PDF of the paper titled Clifford representatives via the uniform algebraic rank, by Myrla Barbosa and 1 other authors
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Abstract:In this paper, we introduce the uniform algebraic rank of a divisor class on a finite graph. We show that it lies between Caporaso's algebraic rank and the combinatorial rank of Baker and Norine. We prove the Riemann-Roch theorem for the uniform algebraic rank, and show that both the algebraic and the uniform algebraic rank are realized on effective divisors. As an application, we use the uniform algebraic rank to show that Clifford representatives always exist. We conclude with an explicit description of such Clifford representatives for a large class of graphs.
    


 
Comments:
20 pages, 3 figures. Comments are welcome!


Subjects:

Algebraic Geometry (math.AG); Combinatorics (math.CO)

Cite as:
arXiv:2406.03987 [math.AG]


 
(or 
arXiv:2406.03987v1 [math.AG] for this version)
          
 
 

https://doi.org/10.48550/arXiv.2406.03987



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                arXiv-issued DOI via DataCite
              







Submission history From: Karl Christ [view email]       [v1]
        Thu, 6 Jun 2024 12:04:07 UTC (28 KB)



 

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