Some Estimates for Plane Cuspidal Curves

Orevkov, S. Y. ; Zaidenberg, M. G.

Séminaire d'algèbre et géométrie, journées singulières et jacobiennes, Cours de l'institut Fourier, no. S24 (1993), pp. 93-116.

EuDML

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     author = {Orevkov, S. Y. and Zaidenberg, M. G.},
     title = {Some {Estimates} for {Plane} {Cuspidal} {Curves}},
     booktitle = {S\'eminaire d'alg\`ebre et g\'eom\'etrie, journ\'ees singuli\`eres et jacobiennes},
     editor = {Gonzalez-Sprinberg, G. and Lejeune-Jalabert, M. and Spivakovsky, M. and Zaidenberg, M. G.},
     series = {Cours de l'institut Fourier},
     pages = {93--116},
     publisher = {Institut des Math\'ematiques Pures - Universit\'e Scientifique et M\'edicale de Grenoble},
     number = {S24},
     year = {1993},
     url = {http://www.numdam.org/item/CIF_1993__S24__93_0/}
}

TY  - CHAP
AU  - Orevkov, S. Y.
AU  - Zaidenberg, M. G.
TI  - Some Estimates for Plane Cuspidal Curves
BT  - Séminaire d'algèbre et géométrie, journées singulières et jacobiennes
AU  - Collectif
ED  - Gonzalez-Sprinberg, G.
ED  - Lejeune-Jalabert, M.
ED  - Spivakovsky, M.
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%A Orevkov, S. Y.
%A Zaidenberg, M. G.
%T Some Estimates for Plane Cuspidal Curves
%B Séminaire d'algèbre et géométrie, journées singulières et jacobiennes
%A Collectif
%E Gonzalez-Sprinberg, G.
%E Lejeune-Jalabert, M.
%E Spivakovsky, M.
%E Zaidenberg, M. G.
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%D 1993
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%F CIF_1993__S24__93_0

Orevkov, S. Y.; Zaidenberg, M. G. Some Estimates for Plane Cuspidal Curves, dans Séminaire d'algèbre et géométrie, journées singulières et jacobiennes, Cours de l'institut Fourier, no. S24 (1993), pp. 93-116. http://www.numdam.org/item/CIF_1993__S24__93_0/

Bibliographie
Cité par

[A] S.S. Abhyankar, "Expansion technique in algebraic geometry", Tata Inst. Fund. Res., Bombay, 1977 | MR

[D] A. Degtyarev, Isotopy classification of complex plane projective curves of degree 5, Leningrad (St. Petersburg) Math. J. 1 (1989), 881-904 | MR | Zbl

[EN] D. Eisenbud, W.D. Neumann, "Three-dimensional link theory and invariants of plane curve singularities". Ann.Math.Stud. 110, Princeton Univ. Press., Princeton 1985 | MR | Zbl

[Fu] T. Fujita, On the topology of non-complete algebraic surfaces, J. Fac. Sci. Univ. Tokyo (Ser 1A), 29 (1982), 503-566 | MR | Zbl

[G] D.A. Gudkov, On the curve of 5th order with 5 cusps, Func. Anal. Appl. 16 (1982), 201-202 | MR | Zbl

[H] F. Hirzebruch, Singularities of algebraic surfaces and characteristic numbers, The Lefschetz Centennial Conf. Part.I (Mexico City1984), Contemp.Math. 58 (1985), 141-155 Amer. Math. Soc, Providence | MR | Zbl

[KNS] R. Kobayashi, S. Nakamura, F. Sakai, A numerical characterization of ball quotients for normal surfaces with branch loci, Proc. Japan Acad. Ser. A Math.Sci. 65 (1989), 238-241 | MR | Zbl

[LZ] V. Lin, M. Zaidenberg, On the number of singular points of a plane affine algebraic curve , Lecture Notes in Math. 1043 (1984), 662-663

[MS] T. Matsuoka, F. Sakai, The degree of rational cuspidal curves, Math. Ann. 285 (1989), 233-247 | MR | Zbl

[Mil] J. Milnor, "Singular points of complex hypersurfaces", Ann.Math.Stud. 61, Princeton Univ. Press, Princeton, 1968 | MR | Zbl

[Miy] Y. Miyaoka, The minimal number of quotient singularities on surfaces with given numerical invariants. Math. Ann. 268 (1984), 159-171 | MR | Zbl

[N] M. Namba, "Geometry of projective algebraic curves", M. Dekker, New York, Basel, 1984 | MR | Zbl

[NR] W. Neumann, L. Rudolph, Unfoldings in knot theory, Math. Ann. 278 (1987), 409-439. | MR | Zbl

W. Neumann, L. Rudolph, Corrigendum, ibid 282 (1988), 349-351 | MR | Zbl

[OZ] S. Yu. Orevkov, M.G. Zaidenberg, Some estimates for plane cuspidal curves, Max-Planck-Institute of Mathematics, Bonn, Preprint MPI/92-63 (1992), 1-13

[Sa] F. Sakai, Singularities of plane curves, Preprint (1991), 1-10 | MR | Zbl

[Sh1] E. Shustin, Real plane algebraic curves with prescribed singularities, Topology 32 (1993), 845-856 | MR | Zbl

[Sh2] E. Shustin, Real plane algebraic curves with many singularities, Proc. Intern. Conf. Real Algebraic Geometry, Rennes, June 24-29, 1991 | MR | Zbl

E. Shustin, Real plane algebraic curves with many singularities, Lect. Notes Math. 1524, Springer, 1992, 389-401 | MR | Zbl

[U] T. Urabe, Singularities in a certain class of quartic surfaces and sextic curves and Dynkin graphs, Canadian Math. Soc. Conf. Proc. 6 (1986), 477-497 | MR | Zbl

[W] I. Wakabayashi, On the logarithmic Kodaira dimension of the complement of a curve in $P^{2}$ , Proc. Japan Acad. Ser. A Math.Sci. 54 (1978), 157-162 | MR | Zbl

[Wal] R.J. Walker, "Algebraic curves", Princeton Univ. Press, Princeton, 1950 | MR | Zbl

[Wall1] C.T.C. Wall, Geometry of quartic curves. Europeen Singularity Project, Preprint No. 57, Liverpool (1994), 1-18 | MR | Zbl

[Wall2] C.T.C. Wall, Highly singular quintic curves, Europeen Singularity Project, Preprint No. 58, Liverpool (1994), 1-36 | MR | Zbl

[Y1] H. Yoshihara, Plane curves whose singular points are cusps,Proc. Amer. Math. Soc. 103 (1988), 737-740 | MR | Zbl

[Y2] H. Yoshihara, Plane curves whose singular points are cusps and triple coverings of $P^{2}$ , Manuscr. Math. 64 (1989), 169-187 | MR | Zbl

[Z] M.G. Zeuthen, Sur les différentes formes des courbes planes du quadrième ordre, Math. Ann. (1893), 408-432 | JFM