TY - JOUR
T1 - The isotopy classification of affine quartic curves
AU - Korchagin, Anatoly B.
AU - Weinberg, David A.
PY - 2002
Y1 - 2002
N2 - 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).
AB - 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).
KW - Algebraic curve
KW - Isotopyclassifi cation
KW - Quartic curve
UR - http://www.scopus.com/inward/record.url?scp=0036520657&partnerID=8YFLogxK
U2 - 10.1216/rmjm/1030539619
DO - 10.1216/rmjm/1030539619
M3 - Article
AN - SCOPUS:0036520657
VL - 32
SP - 255
EP - 347
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
SN - 0035-7596
IS - 1
ER -