科研之友
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摘要
The Hurwitz bound on the size of the -automorphism group Aut(X) of an algebraic curve X of genus g >= 2 defined over a field of zero characteristic is vertical bar Aut(X)vertical bar < 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 16g(4) 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 -automorphism group Aut(X) of a zero 2-rank algebraic curve X defined over an algebraically closed field of characteristic 2 is investigated. The main result is that, if the curve has genus g >= 2 and vertical bar Aut(X)vertical bar > 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.
- 出版日期2010-4
