Symmetric plane curves with nodes and cusps

Mutsuo OKA

doi:10.2969/jmsj/04430375

Mutsuo OKA

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 3 Pages 375-414

DOI https://doi.org/10.2969/jmsj/04430375

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Published: 1992 Received: June 17, 1991 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Heisuke Hironaka on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : A) E. Artin, Theory of braids, Ann. of Math., 48 (1947), 101-126.
B) E. Brieskorn and H. Knörrer, Ebene Algebraische Kurven, Birkhäuser, Basel-Boston-Stuttgart, 1981.
D) P. Deligne, Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abelien, Séminaire Bourbaki, 543 (1979/80).
D-L) I. Dolgachev and A. Libgober, On the fundamental group of the complement to a discriminant variety, in Algebraic Geometry, Lecture Notes in Math., 862, Springer, Berlin-Heidelberg-New York, 1980, pp. 1-25.
F) W. Fulton, On the fundamental group of the complement of a node curve, Ann. of Math., 111 (1980), 407-409.
H) H. Hamm, Lokale topologische Eigenschaf ten komplexer Räume, Math. Ann., 191 (1971), 235-252.
K) E. R. van Kampen, On the fundamental group of an algebraic curve, Amer. J. Math., 55 (1933), 255-260.
Kr) V. I. Krylov, Approximate calculation of integrals (translation), Macmillan, New York, 1962.
M) J. Milnor, Singular Points of Complex Hypersurface, Ann. Math. Stud., Princeton Univ. Press, Princeton, 1968.
O1) M. Oka, On the fundamental group of a reducible curve in P², J. London Math. Soc. (2), 12 (1976), 239-252.
O2)M. Oka, Some plane curves whose complements have non-abelian fundamental groups, Math. Ann., 218 (1975), 55-65.
O3) M. Oka, On the fundamental group of the complement of certain plane curves, J. Math. Soc. Japan, 30 (1978), 579-597.
O4) M. Oka, Principal zeta-function of non-degenerate complete intersection variety, J. Fac. Sci. Univ. Tokyo, 37 (1990), 11-32.
O-S) M. Oka and K. Sakamoto, Product theorem of the fundamental group of a reducible curve, J. Math. Soc. Japan, 30 (1978), 599-602.
T) R. Thom, L'équivalence d'une function différentiable et d'une polynome, Topology, 3 (1965), 297-307.
W) R. J. Walker, Algebraic Curves, Springer, New York-Heidelberg-Berlin, 1949.
Z1) O. Zariski, On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math., 51 (1929), 305-328.
Z2) O. Zariski, On the Poincaré group of rational plane curves, Amer. J. Math., 58 (1929), 607-619.

Right : [A] E. Artin, Theory of braids, Ann. of Math., 48 (1947), 101-126.
[B] E. Brieskorn and H. Knörrer, Ebene Algebraische Kurven, Birkhäuser, Basel-Boston-Stuttgart, 1981.
[D] P. Deligne, Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien, Séminaire Bourbaki, 543 (1979/80).
[D-L] I. Dolgachev and A. Libgober, On the fundamental group of the complement to a discriminant variety, in Algebraic Geometry, Lecture Notes in Math., 862, Springer, Berlin-Heidelberg-New York, 1980, pp. 1-25.
[F] W. Fulton, On the fundamental group of the complement of a node curve, Ann. of Math., 111 (1980), 407-409.
[H] H. Hamm, Lokale topologische Eigenschaften komplexer Räume, Math. Ann., 191 (1971), 235-252.
[K] E. R. van Kampen, On the fundamental group of an algebraic curve, Amer. J. Math., 55 (1933), 255-260.
[Kr] V. I. Krylov, Approximate calculation of integrals (translation), Macmillan, New York, 1962.
[M] J. Milnor, Singular Points of Complex Hypersurface, Ann. Math. Stud., Princeton Univ. Press, Princeton, 1968.
[O1] M. Oka, On the fundamental group of a reducible curve in P², J. London Math. Soc. (2), 12 (1976), 239-252.
[O2] M. Oka, Some plane curves whose complements have non-abelian fundamental groups, Math. Ann., 218 (1975), 55-65.
[O3] M. Oka, On the fundamental group of the complement of certain plane curves, J. Math. Soc. Japan, 30 (1978), 579-597.
[O4] M. Oka, Principal zeta-function of non-degenerate complete intersection variety, J. Fac. Sci. Univ. Tokyo, 37 (1990), 11-32.
[O-S] M. Oka and K. Sakamoto, Product theorem of the fundamental group of a reducible curve, J. Math. Soc. Japan, 30 (1978), 599-602.
[T] R. Thom, L'équivalence d'une function différentiable et d'une polynome, Topology, 3 (1965), 297-307.
[W] R. J. Walker, Algebraic Curves, Springer, New York-Heidelberg-Berlin, 1949.
[Z1] O. Zariski, On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math., 51 (1929), 305-328.
[Z2] O. Zariski, On the Poincaré group of rational plane curves, Amer. J. Math., 58 (1929), 607-619.

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