%0 Journal Article
%T Rank of divisors on hyperelliptic curves and graphs under specialization
%A Shu Kawaguchi
%A Kazuhiko Yamaki
%J Mathematics
%D 2013
%I arXiv
%R 10.1093/imrn/rnu059
%X Let $(G, \omega)$ be a hyperelliptic vertex-weighted graph of genus $g \geq 2$. We give a characterization of $(G, \omega)$ for which there exists a smooth projective curve $X$ of genus $g$ over a complete discrete valuation field with reduction graph $(G, \omega)$ such that the ranks of any divisors are preserved under specialization. We explain, for a given vertex-weighted graph $(G, \omega)$ in general, how the existence of such $X$ relates the Riemann--Roch formulae for $X$ and $(G, \omega)$, and also how the existence of such $X$ is related to a conjecture of Caporaso.
%U http://arxiv.org/abs/1304.6979v3