The isotopy classification of affine quartic curves

Anatoly B. Korchagin, David A. Weinberg

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Abstract

In this paper we obtain the isotopyclassification of affine quartic curves, which contains 647 classes, and the topological classification of pairs (R2, quartic curve), which contains 516 classes (see Theorem 7). We also present the isotopyclassifi cation of real projective quartic curves, which contains 66 classes. We prove that each of these classifications is equivalent to the classification of all real (affine or projective) quartic curves having onlys ingular points, if any, of types A1, A*1, D4 or X9 (see Theorems 5 and 6 and Corollaries 6.1-6.4).

Original languageEnglish
Pages (from-to)255-347
Number of pages93
JournalRocky Mountain Journal of Mathematics
Volume32
Issue number1
DOIs
StatePublished - 2002

Keywords

  • Algebraic curve
  • Isotopyclassifi cation
  • Quartic curve

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