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Experimental Mathematics Volume 16, 2007 - Issue 2
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Original Article

On the Number of Cusps of Rational Cuspidal Plane Curves

Jens Piontkowski Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
Pages 251-255 | Published online: 30 Jan 2011

  • J. Fernández de Bobadilla, I. Luengo- Velasco, A. Melle-Hernández, and A. Némethi. "On Rational Cuspidal Projective Plane Curves." Proc. London Math. Soc. (3) 92:1 (2006), 99–138.
  • T. deJong and G. Pfister. Local Analytic Geometry. Braunschweig: Vieweg, 2000.
  • T. Fenske. "Unendliche Serien ebener rationaler kuspidaler Kurven vom Typ (d, d-k)." PhD diss., University of Bochum, 1999.
  • H. Flenner and M. Zaidenberg. "On a Class of Rational Cuspidal Plane Curves." Manuscripta Math. 89 (1996), 439–459.
  • H. Flenner and M. Zaidenberg. "Rational Cuspidal Plane Curves of Type (d, d-3)." Math. Nachr. 210 (2000), 93–110.
  • G.-M. Greuel, G. Pfister, and H. Schönemann. "Singular 3.0." Software available online from the University of Kaiserslautern (http://www.singular.uni-kl. de), 2005. http://www.singular.uni-kl.de
  • S. Iitaka. "On Logarithmic Kodaira Dimension of Algebraic Varieties." In Complex Analysis and Algebraic Geometry, 175–189. Tokyo: Iwanami Shoten, 1977.
  • V. Kulikov. Mixed Hodge Structures and Singularities, Cambridge Tracts in Math. 132. Cambridge: Cambridge Univ. Press, 1998.
  • V. Lin and M. Zaidenberg. "An Irreducible Simply Connected Curve in ℂ2 Is Equivalent to a Quasihomogeneous Curve." Soviet Math. Dokl. 28 (1978), 200–204.
  • T. Matsuoka and F. Sakai. "The Degree of Rational Cuspidal Curves." Math. Ann. 285 (1989), 233–247.
  • M. Namba. Geometry of Projective Algebraic Curves. New York: Dekker 1984.
  • A. Némethi. "The Signature of f(x, y)+zN." In Singularity Theory (Liverpool, 1996), 131–149, London Math. Soc. Lecture Note Ser. 263. Cambridge: Cambridge Univ. Press, 1999.
  • S. Orevkov and M. Zaidenberg. "On the Number of Singular Points of Plane Curves." arXiv:alg-geom/9507005, 1995.
  • Jens Piontkowski. Computer program available online (http://www.expmath.org/expmath/volumes/ 16/16.2/Piontkowski/supplement.tar), 2007. http://www.expmath.org/expmath/volumes/16/16.2/Piontkowski/supplement.tar
  • M. Saito. "Exponents of an Irreducible Plane Curve Singularity." arXiv: math.AG/0009133, 2000.
  • K. Tono. "On the Number of the Cusps of Cuspidal Plane Curves." Math. Nachr. 278 (2005), 216–221.
  • I. Wakabayashi. "On the Logarithmic Kodaira Dimension of the Complement of a Curve in ℙ2." Proc. Japan Acad. 54A (1978), 157–162.
  • H. Yoshihara. "Plane Curves Whose Singular Points Are Cusps and Triple Coverings of P2." Manuscripta Math. 64 (1989), 169–187.
  • H. Yoshihara. "A Note on the Existence of Some Curves." In Algebraic Geometry and Commutative Algebra in Honor of M. Nagata, edited by H. Hijikata et al., 801–804. Tokyo: Kinokuniya, 1997.

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