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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Rational curve with one cusp
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by Hisao Yoshihara PDF
Proc. Amer. Math. Soc. 89 (1983), 24-26 Request permission

Abstract:

In this paper we shall give new examples of plane curves $C - \{ P\} \cong {{\mathbf {A}}^1}$ satisfying $C - \{ P\} \cong {{\mathbf {A}}^1}$ for some point $P \in C$ by using automorphisms of open surfaces.
References
  • Shreeram S. Abhyankar and Tzuong Tsieng Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148–166. MR 379502
  • Julian Lowell Coolidge, A treatise on algebraic plane curves, Dover Publications, Inc., New York, 1959. MR 0120551
  • Shigeru Iitaka, Algebraic geometry, North-Holland Mathematical Library, vol. 24, Springer-Verlag, New York-Berlin, 1982. An introduction to birational geometry of algebraic varieties. MR 637060
  • Shuichiro Tsunoda, The structure of open algebraic surfaces and its application to plane curves, Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), no. 4, 230–232. MR 618231
  • Hisao Yoshihara, On plane rational curves, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 4, 152–155. MR 533711
  • —, Projective plane curves and the automorphism groups of their complements (to appear).
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 24-26
  • MSC: Primary 14H45; Secondary 14H20
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0706501-0
  • MathSciNet review: 706501