Critical Groups of Graphs with Dihedral Actions
This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to use the Deuring-Shafarevich formula in order to analyze the ramification of hyperelliptic curves that admit extra automorphisms and use this data to impose restrictions on the genera and 2-ranks of such curves. We also show how some of the techniques and results carry over to the case where our base field is of characteristic p > 2.
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Glass, Darren and Criel Merino. "Critical Groups of Graphs with Dihedral Actions." European Journal of Combinatorics 39 (July 2014), 95-112.
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Original version is available from the publisher at: http://www.journals.elsevier.com/european-journal-of-combinatorics/