Título inglés |
Curves in P2(C) with 1-dimensional symmetry. |
Título español |
Curvas en P2(C) con simetría 1-dimensional. |
Autor/es |
Plessis, A. A. du ; Wall, Charles Terence Clegg |
Organización |
Mat. Inst. Aarhus Univ., Aarhus, Dinamarca;Dep. Pure Mat. Univ. Liverpool, Liverpool, Reino Unido |
Revista |
1139-1138 |
Publicación |
1999, 12 (1): 117-131, 10 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding curves are given in the cases d ≤ 6. We also show that the projective classification of these curves coincides -except in the case of the group action with weights [-1,0,1] - with the classification of the singular points. The sum t of the Tjurina numbers of the singular points is either d2 - 3d + 3 or d2 - 3d + 2 while, for d ≥ 5, if there is no group action we have t ≤ d2 - 4d + 7. We give m = t in the semi-simple case; in the unipotent case, we determine the values of both m and t. In the semi-simple case, we show that the unfolding mentioned above is also topologically versal if d ≥ 6; in the unipotent case this holds at least if d = 6. |
Clasificación UNESCO |
120410 |
Palabras clave español |
Espacio proyectivo complejo ; Simetría |
Código MathReviews |
MR1698902 |
Código Z-Math |
Zbl 0969.14022 |
Acceso al artículo completo |