Classification of sextics of torus type. (English) Zbl 1062.14036

From the introduction: We consider an irreducible sextic \(C\) of torus type defined by \(\{(X,Y,Z)\in\mathbb{P}^2;\;F_2(X,Y,Z)^3+ F_3(X,Y, Z)^2=0\}\). We say that \(C\) is tame if its singularities are contained in \(V(F_2)\cap V(F_3)\). For tame sextics of torus type, there are 25 local singularity types among which 20 appear on irreducible sextics of torus type [D. T. Pho, Kodai Math. J. 24 (2), 259–284 (2000; Zbl 1072.14031)]. As global singularities, there are 43 configurations of singularities on irreducible tame torus curves. In this paper, we complete the classification of configurations of the singularities on irreducible sextics of torus type. We show that there exist 121 configurations and there are 5 pairs and a triple of configurations for which the corresponding moduli spaces coincide, ignoring the respective torus decomposition.


14H20 Singularities of curves, local rings
14H45 Special algebraic curves and curves of low genus


Zbl 1072.14031
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