Table of Contents
Geometry
Volume 2013, Article ID 369420, 6 pages
http://dx.doi.org/10.1155/2013/369420
Research Article

Galois Group at Each Point for Some Self-Dual Curves

1Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
2Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan

Received 10 October 2012; Accepted 21 December 2012

Academic Editor: Michel Planat

Copyright © 2013 Hiroyuki Hayashi and Hisao Yoshihara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Miura, “Field theory for function fields of singular plane quartic curves,” Bulletin of the Australian Mathematical Society, vol. 62, no. 2, pp. 193–204, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. H. Yoshihara, “Function field theory of plane curves by dual curves,” Journal of Algebra, vol. 239, no. 1, pp. 340–355, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Yoshihara, “Galois points for plane rational curves,” Far East Journal of Mathematical Sciences, vol. 25, no. 2, pp. 273–284, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. Yoshihara, “Rational curve with Galois point and extendable Galois automorphism,” Journal of Algebra, vol. 321, no. 5, pp. 1463–1472, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J.-P. Serre, Topics in Galois Theory, vol. 1 of Research Notes in Mathematics, Jones & Bartlett, Boston, Mass, USA, 1992. View at MathSciNet
  6. F. Cukierman, “Monodromy of projections,” Matemática Contemporânea, vol. 16, pp. 9–30, 1999 (Portuguese), 15th School of Algebra. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Harris, “Galois groups of enumerative problems,” Duke Mathematical Journal, vol. 46, no. 4, pp. 685–724, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Yoshihara, “Applications of Plücker's formula,” Sûgaku, vol. 32, no. 4, pp. 367–369, 1980 (Japanese). View at Google Scholar · View at MathSciNet
  9. S. Iitaka, K. Ueno, and Y. Namikawa, Descartes No Seishin To Daisûkika, NipponHyoron Sha, Tokyo, Japan, 1980.
  10. M. Oka, “Elliptic curves from sextics,” Journal of the Mathematical Society of Japan, vol. 54, no. 2, pp. 349–371, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. P. Pirola and E. Schlesinger, “Monodromy of projective curves,” Journal of Algebraic Geometry, vol. 14, no. 4, pp. 623–642, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. Fulton, Algebraic Curves, Mathematics Lecture Notes Series, Benjamin, New York, NY, USA, 1969. View at MathSciNet
  13. K. Miura and H. Yoshihara, “Field theory for function fields of plane quartic curves,” Journal of Algebra, vol. 226, no. 1, pp. 283–294, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet