×

On classifications of rational sextic curves. (English) Zbl 1348.14086

Summary: In this paper, we extend the Yang’s list of reduced sextic plane curves to rational irreducible projective plane curves of type (6, 3, 1).

MSC:

14H45 Special algebraic curves and curves of low genus
14R20 Group actions on affine varieties
14H30 Coverings of curves, fundamental group
14H50 Plane and space curves

References:

[1] Brieskorn, E.; Knörrer, H., Plane Algebraic Curves (1986), Birkhäuser: Birkhäuser Basel · Zbl 0588.14019
[2] de Jong, Theo; Pfister, Gerhard, Local Analytic Geometry (2000), Vieweg · Zbl 0959.32011
[3] Yoshihara, H., On plane rational curves, Proc. Jpn. Acad., 55, A, 152-155 (1979) · Zbl 0432.14019
[4] Yoshihara, H., Rational curves with one cusps, Proc. Am. Math. Soc., 100, 405-406 (1987) · Zbl 0632.14025
[5] Yoshihara, H., Plane curves whose singular points are cusps, Proc. Am. Math. Soc., 103, 737-740 (1988) · Zbl 0698.14021
[6] Yang, J.-G., Sextic curves with simple singularities, Tohoko Math. J., 48, 203-227 (1996) · Zbl 0866.14014
[7] Saleem, M., On the Classification of Rational Plane Curves of Types (d, m) (2011), Lambert Acad. Publishing, ISBN: 978-3-8443-9988-2
[8] Sakai, F.; Saleem, M., Rational plane curves of type \((d, d - 2)\), Saitama Math. J., 22, 11-34 (2004) · Zbl 1079.14042
[9] Sakai, F.; Saleem, M.; Tono, K., Hyperelliptic plane curves of type \((d, d - 2)\), Contribut. Algebra Geometry, 51, 1, 31-44 (2010) · Zbl 1184.14053
[10] Matsuoka, T.; Sakai, F., The degree of rational cuspidal plane curves, Math. Ann., 285, 233-247 (1989), 657-673 · Zbl 0661.14023
[11] Flenner, H.; Zaidenberg, M., On a class of rational cuspidal plane curves, Manuscripta Math., 89, 439-460 (1996) · Zbl 0868.14014
[12] Flenner, H.; Zaidenberg, M., Rational cuspidal plane curves of type \((d, d - 3)\), Math. Nach., 210, 93-110 (2000) · Zbl 0948.14020
[13] Fenske, T., Rational 1- and 2-cuspidal plane curves, Beiträge Alg. Geometrie, 40, 2, 309-329 (1999) · Zbl 0959.14012
[14] Sakai, F.; Tono, K., Rational cuspidal curves of type \((d, d - 2)\) with one or two cusps, Osaka J. Math., 37, 415-504 (2000) · Zbl 0969.14020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.