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- Title
Rank of Divisors on Hyperelliptic Curves and Graphs Under Specialization.
- Authors
Shu Kawaguchi; Kazuhiko Yamaki
- Abstract
Let (G, ω) be a hyperelliptic vertex-weighted graph of genus g≥ 2. We give a characterization of (G, ω) for which there exists a smooth projective curve X of genus g over a complete discrete valuation field with reduction graph (G, ω) such that the ranks of any divisors are preserved under specialization. We explain, for a given vertex-weighted graph (G, ω) in general, how the existence of such X relates the Riemann-Roch formulae for X and (G, ω), and also how the existence of such X is related to a problem by Caporaso.
- Subjects
DIVISOR theory; HYPERELLIPTIC integrals; GRAPH theory; RIEMANN-Roch theorems; PROJECTIVE curves
- Publication
IMRN: International Mathematics Research Notices, 2015, Issue 12, p4121
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnu059