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Algebraic curves with a large non-tame automorphism group fixing no point

Author(s): M. Giulietti; G. Korchmáros
Journal: Trans. Amer. Math. Soc. 362 (2010), 5983-6001.
MSC (2010): Primary 14H37
Posted: June 10, 2010
MathSciNet review: 2661505
Retrieve article in: PDF

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Abstract: Let $\mathbb{K}$ be an algebraically closed field of characteristic , and let $\mathcal{X}$ be a curve over $\mathbb{K}$ of genus $g\ge 2$ . Assume that the automorphism group $\mathrm{Aut}(\mathcal{X})$ of $\mathcal{X}$ over $\mathbb{K}$ fixes no point of $\mathcal{X}$ . The following result is proven. If there is a point on $\mathcal{X}$ whose stabilizer in $\mathrm{Aut}(\mathcal{X})$ contains a -subgroup of order greater than , then $\mathcal{X}$ is birationally equivalent over $\mathbb{K}$ to one of the irreducible plane curves (II), (III), (IV), (V) listed in the Introduction.

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