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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: M. Giulietti and G. Korchmáros
Journal: Trans. Amer. Math. Soc. 362 (2010), 5983-6001
MSC (2010): Primary 14H37
Published electronically: June 10, 2010
MathSciNet review: 2661505
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Abstract: Let $ \mathbb{K}$ be an algebraically closed field of characteristic $ p>0$, 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 $ P$ on $ \mathcal{X}$ whose stabilizer in $ \mathrm{Aut}(\mathcal{X})$ contains a $ p$-subgroup of order greater than $ gp/(p-1)$, 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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Additional Information

M. Giulietti
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia, Italy
Email: giuliet@dipmat.unipg.it

G. Korchmáros
Affiliation: Dipartimento di Matematica, Università della Basilicata, Contrada Macchia Romana, 85100 Potenza, Italy
Email: gabor.korchmaros@unibas.it

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05025-1
PII: S 0002-9947(2010)05025-1
Keywords: Algebraic curves, positive characteristic, automorphism groups
Received by editor(s): August 29, 2008
Received by editor(s) in revised form: February 19, 2009
Published electronically: June 10, 2010
Additional Notes: This research was supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.