An explicit family of curves with trivial automorphism groups

Author:
Peter Turbek

Journal:
Proc. Amer. Math. Soc. **122** (1994), 657-664

MSC:
Primary 14H55

DOI:
https://doi.org/10.1090/S0002-9939-1994-1242107-2

MathSciNet review:
1242107

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that a generic compact Riemann surface of genus greater than two admits only the identity automorphism; however, examples of such Riemann surfaces with their defining algebraic equations have not appeared in the literature. In this paper we give the defining equations of a doubly infinite, two-parameter family of projective curves (Riemann surfaces if defined over the complex numbers), whose members admit only the identity automorphism.

**[1]**W. L. Bailey,*On the automorphism group of a generic curv e of genus greater than*2 , J. Math. Kyoto Univ.**1**(1961), 101-108.**[2]**H. M. Farkras and I. Kra,*Riemann surfaces*, 2nd ed., Graduate Texts in Math., vol. 71, Springer-Verlag, Berlin and New York, 1991.**[3]**William Fulton,*Algebraic curves. An introduction to algebraic geometry*, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes written with the collaboration of Richard Weiss; Mathematics Lecture Notes Series. MR**0313252****[4]**Leon Greenberg,*Maximal Fuchsian groups*, Bull. Amer. Math. Soc.**69**(1963), 569–573. MR**0148620**, https://doi.org/10.1090/S0002-9904-1963-11001-0**[5]**Subhashis Nag,*The complex analytic theory of Teichmüller spaces*, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1988. A Wiley-Interscience Publication. MR**927291****[6]**Ivan Niven and Herbert S. Zuckerman,*An introduction to the theory of numbers*, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR**0195783**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
14H55

Retrieve articles in all journals with MSC: 14H55

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1242107-2

Article copyright:
© Copyright 1994
American Mathematical Society