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 language | English |
|---|---|
| Pages (from-to) | 255-347 |
| Number of pages | 93 |
| Journal | Rocky Mountain Journal of Mathematics |
| Volume | 32 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2002 |
Keywords
- Algebraic curve
- Isotopyclassifi cation
- Quartic curve
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Cite this
Korchagin, A. B., & Weinberg, D. A. (2002). The isotopy classification of affine quartic curves. Rocky Mountain Journal of Mathematics, 32(1), 255-347. https://doi.org/10.1216/rmjm/1030539619