SMOOTHNESS AND IRREDUCIBILITY OF VARIETIES OF PLANE-CURVES WITH NODES AND CUSPS

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Abstract

Let V (d, m, k) be the variety of plane projective irreducible curves of degree d with m nodes and k cusps as their only singularities. We prove that V (d, m, k) is non-empty, non-singular and irreducible when m + 2k < αd2, where α is some absolute explicit constant. This estimate is optimal with respect to the exponent of d
Original languageEnglish
Pages (from-to)235-253
Number of pages19
JournalBulletin de la Societe Mathematique de France
Volume122
Issue number2
DOIs
StatePublished - 1994

Keywords

  • FAMILY OF SINGULAR PLANE ALGEBRAIC CURVES
  • LINEAR SYSTEM
  • RIEMANN-ROCH THEOREM
  • IRREDUCIBILITY

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