Galois points for a normal hypersurface

Authors:
Satoru Fukasawa and Takeshi Takahashi

Journal:
Trans. Amer. Math. Soc. **366** (2014), 1639-1658

MSC (2010):
Primary 14J70, 12F10

Published electronically:
October 23, 2013

MathSciNet review:
3145745

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Abstract | References | Similar Articles | Additional Information

Abstract: A Galois point for a hypersurface is a point from which the projection induces a Galois extension of function fields. The purpose of this article is to determine the set of Galois points for a hypersurface with in characteristic zero: In fact, if is not a cone, we give a sharp upper bound for the cardinality of in terms of and , and completely classify attaining the bound. We determine also when is a cone. To achieve our purpose, we prove a certain hyperplane section theorem on a Galois point in arbitrary characteristic. The hyperplane section theorem has other important applications: For example, we can classify the Galois group induced by a Galois point in arbitrary characteristic and determine the distribution of Galois points for a Fermat hypersurface of degree in characteristic .

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Additional Information

**Satoru Fukasawa**

Affiliation:
Department of Mathematical Sciences, Faculty of Science, Yamagata University, Kojirakawa-Machi 1-4-12, Yamagata 990-8560, Japan

Email:
s.fukasawa@sci.kj.yamagata-u.ac.jp

**Takeshi Takahashi**

Affiliation:
Division of General Education, Nagaoka National College of Technology, 888 Nishikatakai, Nagaoka, Niigata 940-8532, Japan

Email:
takeshi@nagaoka-ct.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-2013-05875-8

Keywords:
Galois point,
hypersurface

Received by editor(s):
May 9, 2010

Received by editor(s) in revised form:
March 29, 2012

Published electronically:
October 23, 2013

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.