Maximally symmetric stable curves II

Details Maximally symmetric stable curves II Maximally symmetric stable curves II

2006-08-31

arxiv.org/abs/math/0608799v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We find a sharp bound for the order of the automorphism group of a stable curve of genus $g$ with $3g-3$ nodes, and a sharp bound for the order of the automorphism group of such a curve with all smooth components. Combined with the results of our article math.CO/0608645 we find that graph theoretically, the cubic graph with a given number of vertices and most automorphisms is simple, but algebro-geometrically, the stable curves with $3g-3$ nodes that have the most automorphisms have non-simple dual graph.

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