Advertisement

Mathematische Annalen

, Volume 285, Issue 2, pp 233–247 | Cite as

The degree of rational cuspidal curves

  • Takashi Matsuoka
  • Fumio Sakai
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AM] Abyankar, S., Moh, T.: Embeddings of the line in the plane. J. Reine Angew. Math.276, 148–166 (1975)Google Scholar
  2. [BPV] Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Berlin, Heidelberg, New York: Springer 1984Google Scholar
  3. [BK] Brieskorn, E., Knörrer, H.: Plane algebraic curves. Basel, Boston, Stuttgart: Birkhäuser 1986Google Scholar
  4. [C] Coolidge, J.L.: A treatise on algebraic plane curves. Oxford: Oxford Univ. Press 1928Google Scholar
  5. [G] Gizatullin, M.H.: Review to the paper [MS]. Math. Review 82k. No. 14013 (1982)Google Scholar
  6. [GD] Gizatullin, M.H., Danilov, V.I.: Automorphisms of affine surfaces. I. Math. USSR Izv.9, 493–534 (1975)Google Scholar
  7. [I 1] Iitaka, S.: Algebraic geometry. Berlin Heidelberg New York: Springer 1981Google Scholar
  8. [I 2] Iitaka, S.: On irreducible plane curves. Saitama Math. J.1, 47–63 (1983)Google Scholar
  9. [Iv] Ivinskis, K.: Normale Flächen und die Miyaoka-Kobayashi Ungleichung Diplomarbeit Bonn 1985Google Scholar
  10. [H] Hirzebruch, F.: Singularities of algebraic surfaces and characteristic numbers. Contemp. Math.58, 141–155 (1986)Google Scholar
  11. [Ka] Kashiwara, H.: Fonctions rationelles de type (0,1) sur l'espace projectif complexe a deux dimensions. Osaka Math. J.24, 521–577 (1987)Google Scholar
  12. [Ki] Kizuka, T.: Rational functions of C*-type on the two-dimensional complex projective space. Tohoku Math. J.38, 123–178 (1986)Google Scholar
  13. [Ko] Kohno, T.: Differential forms and the fundamental group of the complement of hypersurfaces. Proc. Symp. Pure Math.40, 655–662 (1983)Google Scholar
  14. [La 1] Laufer, H.: Normal two-dimensional singularities. Ann. Math. Stud.71 (1971)Google Scholar
  15. [La 2] Laufer, H.: On μ for surface singularities. Proc. Symp. Pure Math.30, 45–50 (1977)Google Scholar
  16. [Li] Libgober, A.: Alexander invariants on plane algebraic curves. Proc. Symp. Pure Math.40, 135–143 (1983)Google Scholar
  17. [Mil] Milnor, J.: Singular points of complex hypersurfaces. Ann. Math. Stud.61 (1968)Google Scholar
  18. [Mim] Miyanishi, M.: Lectures on curves on rational and unirational surfaces. Bombay: Tata Institute of Fundamental Research 1978Google Scholar
  19. [MS] Miyanishi, M., Sugie, T.: On a projective plane curve whose complement has logarithmic Kodaira dimension−∞. Osaka J. Math.18, 1–11 (1981)Google Scholar
  20. [Miy] Miyaoka, Y.: The maximal number of quotient singularities on surfaces with given numerical invariants. Math. Ann.26, 159–171 (1984)Google Scholar
  21. [MM] Mohan Kumar, N., Murthy, M.P.: Curves with negative self intersection on rational surfaces. J. Math. Kyoto Univ.22, 767–777 (1983)Google Scholar
  22. [Nag] Nagata, M.: On rational surfaces. I. Mem. Coll. Sci. Univ. Kyoto32, 351–370 (1960)Google Scholar
  23. [Nam] Namba, M.: Geometry of projective algebraic curves. New York, Basel: Dekker 1984Google Scholar
  24. [R] Randell, R.: Some topology of Zariski surfaces. (Lecture Notes in Math. 788, pp. 145–164.) Berlin Heidelberg New York: Springer 1979Google Scholar
  25. [Sa] Saito, H.: Fonctions entières qui se reduisent à certains polynomes I. Osaka J. Math.9, 293–332 (1972)Google Scholar
  26. [Sak 1] Sakai, F.: Semi-stable curves on algebraic surfaces and logarithmic pluricanonical maps. Math. Ann.254, 89–120 (1980)Google Scholar
  27. [Sak 2] Sakai, F.: Weil divisors on normal surfaces. Duke Math. J.51, 877–887 (1984)Google Scholar
  28. [Sum] Suzuki, M.: Propriétés topologiques des polynomes de deux variables complexes, et automorphisms algébriques de l'espace C2. J. Math. Soc. Japan26, 241–257 (1974)Google Scholar
  29. [Sus] Suzuki, S.: Birational geometry of birational pairs. Comment. Math. Univ. St. Paul32, 85–106 (1983)Google Scholar
  30. [T] Tsunoda, S.: The complements of projective plane curves. RIMS-Kokyuroko446, 48–55 (1981)Google Scholar
  31. [Y 1] Yoshihara, H.: A problem on plane rational curves (in Japanese). Sugaku31, 256–261 (1979)Google Scholar
  32. [Y 2] Yoshihara, H.: On plane rational curves. Proc. Japan Acad. Ser. A55, 152–155 (1979)Google Scholar
  33. [Y 3] Yoshihara, H.: Rational curves with one cusp. Proc. Am. Math. Soc.89, 24–26 (1983)Google Scholar
  34. [Y 4] Yoshihara, H.: Rational curves with one cusp. II. Proc. Am. Math. Soc.100, 405–406 (1987)Google Scholar
  35. [Y 5] Yoshihara, H.: A note on the existence of some curves. (Algebraic geometry and commutative algebra in honor of M. Nagata, pp. 801–804.) Tokyo: Kinokuniya 1987Google Scholar
  36. [Y 6] Yoshihara, H.: Plane curves whose singular points are cusps and triple coverings of ℙ2. PreprintGoogle Scholar
  37. [Z 1] Zariski, O.: On the linear connection index of the algebraic surfacez n =f(x,y). Proc. Nat. Acad. Sci.15, 494–501 (1929)Google Scholar
  38. [Z 2] Zariski, O.: Studies in equisingularity. III. Am. J. Math.90, 961–1023 (1968)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Takashi Matsuoka
    • 1
  • Fumio Sakai
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceSaitama UniversityUrawaJapan

Personalised recommendations