Dihedral coverings of algebraic surfaces and their application

Author:
Hiro-o Tokunaga

Journal:
Trans. Amer. Math. Soc. **352** (2000), 4007-4017

MSC (2000):
Primary 14E20; Secondary 14E15

Published electronically:
March 15, 2000

MathSciNet review:
1675238

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Abstract | References | Similar Articles | Additional Information

In this article, we study dihedral coverings of algebraic surfaces branched along curves with at most simple singularities. A criterion for a reduced curve to be the branch locus of some dihedral covering is given. As an application we have the following:

Let be a reduced plane curve of even degree having only nodes and cusps. If , then is non-abelian.

Note that Nori's result implies that is abelian, provided that .

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Additional Information

**Hiro-o Tokunaga**

Affiliation:
Department of Mathematics and Information Science, Kochi University, Kochi 780-8520, Japan

Address at time of publication:
Department of Mathematics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397 Japan

Email:
tokunagamath.kochi-u.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9947-00-02524-1

Received by editor(s):
June 20, 1998

Published electronically:
March 15, 2000

Additional Notes:
This research is partly supported by the Grant-in-Aid for Encouragement of Young Scientists 09740031 from the Ministry of Education, Science and Culture.

Article copyright:
© Copyright 2000
American Mathematical Society