On quartic surfaces and sextic curves with certain singularities (Q800441)

The classification of the singularities lying on a normal surface in \(P^ 3\) of small degree is a subject with classical roots. For instance one knows all possible configurations of singularities lying on a cubic surface. In this paper the author classifies completely the singularities of a normal quartic surface (resp. of a sextic curve in \(P^ 2)\) having one of the following prescribed singularities: a simple elliptic singularity of type \(\tilde E_ 7\) or \(\tilde E_ 6\), a cusp singularity of type \(T_{2,4,5}\) or \(T_{3,3,4}\), a unimodular exceptional singularity of type \(Z_{11}\) or \(Q_{10}\) (resp. \(\tilde E_ 7\), \(T_{2,4,5}\), or \(Z_{11})\). In an earlier paper of the same author the classification of the singularities of normal quartic surfaces and of sextic curves with one of the singularities \(\tilde E_ 8\), \(T_{2,3,7}\) or \(E_{12}\) was given [see the author, ''On quartic surfaces and sextic curves with singularities of type \(\tilde E_ 8\), \(T_{2,3,7}\), \(E_{12}\)'' (Preprint 1983)]. Finally, we note that this paper gives no details concerning the proofs of the results.