Automorphism groups of algebraic curves with p-rank zero
- Autores: Massimo Giulietti, Gábor Korchmáros
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 2, 2010, págs. 277-296
- Idioma: inglés
- Enlaces
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Resumen
The Hurwitz bound on the size of the K-automorphism group Aut(X) of an algebraic curve X of genus g 2 defined over a field K of zero characteristic is |Aut(X)| 84(g - 1). For a positive characteristic, algebraic curves can have many more automorphisms than expected from the Hurwitz bound. There even exist algebraic curves of arbitrary high genus g with more than 16g4 automorphisms. It has been observed on many occasions that the most anomalous examples of algebraic curves with very large automorphism groups invariably have zero p-rank. In this paper, the K-automorphism group Aut(X) of a zero 2-rank algebraic curve X defined over an algebraically closed field K of characteristic 2 is investigated. The main result is that, if the curve has genus g 2 and |Aut(X)| > 24g(g - 1), then Aut(X) has a fixed point on X, apart from a few exceptions. In the exceptional cases, the possibilities for Aut(X) and g are determined.
