Sextic curves with simple singularities
In this paper the author studies the configuration of simple singularities in a reduced sixtic curve in \(\mathbb{P}^2\). Recall that singularities are described by their dual graph in an embedded resolution of singularities and simple singularities are in correspondence with simple Dynkin diagrams, of type \(A_i\) \((i\geq 1)\), \(D_j\) \((j\geq 4)\) and \(E_k\) \((k=6,7,8)\). The main theorem in this article is: There exists a reduced sixtic curve in \(\mathbb{P}^2\) with only simple singularities given by a finite Dynkin graph \(G\) if and only if \(G\) is a subgraph of a graph listed by the author. For the proof the author uses full version of Nikulin's embedding theorem of even lattices.
scientific article; zbMATH DE number 927276
scientific article