On some quartic surfaces with triple lines (Q717827)

Inspired by works of Bydzovsky and Abhyankar, the paper investigates the tangent planes at the points of a triple line of a quartic non-conic algebraic surface. In particular, characterizations of the singularities of the triple line with respect to the type of the corresponding tangent cone, their number and the number of lines passing through these points are given. This way, the paper provides new information on the (non-completely solved yet) problem of classifying quartic algebraic surfaces.