Zariski pairs, fundamental groups and Alexander polynomials

Enrique ARTAL BARTOLO; Jorge CARMONA RUBER

doi:10.2969/jmsj/05030521

Enrique ARTAL BARTOLO, Jorge CARMONA RUBER

著者情報

キーワード: Fundamental group, plane curve, Alexander polynomial

ジャーナルフリー

1998 年 50 巻 3 号 p. 521-543

DOI https://doi.org/10.2969/jmsj/05030521

詳細

Published: 1998 Received: 1996/01/30 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: キーワード情報訂正内容: Right : Fundamental group, plane curve, Alexander polynomial

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : A1) E. Artal, Les couples de Zariski, J. Algebraic Geom. 3 (1994), 223-247.
A2) E. Artal: Forme de Jordan de la monodromie des singularitées superisolées de surfaces, Mem, Amer. Math. Soc., vol. 109, no. 525, American Mathematical Society, Providence RI.
C) J.-I. Cogolludo, Grupo fundamental del complementario de curvas proyectivas planas con nodos y cúspides, Preprint (1995).
D) A. Degtyarev, Alexander polynomial of a curve of degree six, J. Knot Theory Ramifications 3 (1994), 439-454.
F) T. Fujita, On the topology of non-complete surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), 503-566.
GAP) M. Schönert et al., GAP version 3.4, 4th edition, Lehrstuhl D für Mathematik, RWTH Aachen, 1995.
Li) A. Libgober, Alexander polynomials of plane algebraic curves and cyclic multiple planes, Duke Math. J. 49 (1982), 833-851.
Lu) I. Luengo, The μ-constant stratum is not smooth, Invent. Math. 90 (1987), 139-152.
M) J. Milnor, Singular Points of Complex Hypersurfaces, Annals of Mathematics Sudies 61, Princeton Univ. Press, Princeton N.Y., 1968.
O1) M. Oka, Symmetric plane curves with nodes and cusps, J. Math. Soc. Japan 44 (1992), 375-414.
O2) M. Oka, Two transforms of plane curves and their fundamental groups, Preprint (1995).
Sh) I. Shimada, A note on Zariski pairs, Preprint MPI für Mathematik (1995).
St) J. Stevens, On the μ-constant Stratum and the V-filtration: an Example, Math. Z. 201 (1989), 139-144.
T) H.-O Tokunaga, Some examples of Zariski pairs arising from certain elliptic K3 surfaces, Preprint (1995).
W) R.-J. Walker, Algebraic curves, Princeton Math. Series 13, Princeton University Press, Princeton NJ.
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 irregularity of cyclic multiple planes, Ann. Math. 32 (1931), 445-489.
Z3) O. Zariski, The topological discriminant group of a Riemann surface of genus p, Amer. J. Math. 59 (1937), 335-358.

Right : [A1] E. Artal, Les couples de Zariski, J. Algebraic Geom. 3 (1994), 223-247.
[A2] E. Artal, Forme de Jordan de la monodromie des singularitées superisolées de surfaces, Mem, Amer. Math. Soc., vol. 109, no. 525, American Mathematical Society, Providence RI.
[C] J. -I. Cogolludo, Grupo fundamental del complementario de curvas proyectivas planas con nodos y cúspides, Preprint (1995).
[D] A. Degtyarev, Alexander polynomial of a curve of degree six, J. Knot Theory Ramifications 3 (1994), 439-454.
[F] T. Fujita, On the topology of non-complete surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), 503-566.
[GAP] M. Schönert et al., GAP version 3.4, 4th edition, Lehrstuhl D für Mathematik, RWTH Aachen, 1995.
[Li] A. Libgober, Alexander polynomials of plane algebraic curves and cyclic multiple planes, Duke Math. J. 49 (1982), 833-851.
[Lu] I. Luengo, The μ-constant stratum is not smooth, Invent. Math. 90 (1987), 139-152.
[M] J. Milnor, Singular Points of Complex Hypersurfaces, Annals of Mathematics Sudies 61, Princeton Univ. Press, Princeton N. Y., 1968.
[O1] M. Oka, Symmetric plane curves with nodes and cusps, J. Math. Soc. Japan 44 (1992), 375-414.
[O2] M. Oka, Two transforms of plane curves and their fundamental groups, Preprint (1995).
[Sh] I. Shimada, A note on Zariski pairs, Preprint MPI für Mathematik (1995).
[St] J. Stevens, On the μ-constant Stratum and the V-filtration: an Example, Math. Z. 201 (1989), 139-144.
[T] H. -O Tokunaga, Some examples of Zariski pairs arising from certain elliptic K3 surfaces, Preprint (1995).
[W] R. -J. Walker, Algebraic curves, Princeton Math. Series 13, Princeton University Press, Princeton NJ.
[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 irregularity of cyclic multiple planes, Ann. Math. 32 (1931), 445-489.
[Z3] O. Zariski, The topological discriminant group of a Riemann surface of genus p, Amer. J. Math. 59 (1937), 335-358.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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