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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Fixed points of automorphisms of compact Riemann surfaces and higher-order Weierstrass points

Authors: Ryutaro Horiuchi and Tomihiko Tanimoto
Journal: Proc. Amer. Math. Soc. 105 (1989), 856-860
MSC: Primary 30F35; Secondary 14F07, 14H99
MathSciNet review: 957265
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Abstract | References | Similar Articles | Additional Information

Abstract: A sufficient condition for fixed points of an automorphism of prime order on a compact Riemann surface to be higher-order Weierstrass points is given. This leads us to a complete study of the cases where the prime orders are small.

References [Enhancements On Off] (What's this?)

  • [1] Robert D. M. Accola, On generalized Weierstrass points on Riemann surfaces, Modular functions in analysis and number theory, Lecture Notes Math. Statist., vol. 5, Univ. Pittsburgh, Pittsburgh, PA, 1983, pp. 1–19. MR 732958 (85f:14016)
  • [2] Andrei Duma, Holomorphe Differentiale höherer Ordnung auf kompakten Riemannschen Flächen, Schr. Math. Inst. Univ. Münster (2) 14 (1978), i+40 (German). MR 515153 (80g:14026)
  • [3] Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745 (82c:30067)
  • [4] Ignacio Guerrero, Automorphisms of compact Riemann surfaces and Weierstrass points, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 215–224. MR 624815 (82j:14027)
  • [5] Joseph Lewittes, Automorphisms of compact Riemann surfaces, Amer. J. Math. 85 (1963), 734–752. MR 0160893 (28 #4102)

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Additional Information

PII: S 0002-9939(1989)0957265-2
Article copyright: © Copyright 1989 American Mathematical Society

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