Rational Tacnodal and Oscnodal Quartic Curves Considered as Plane Sections of Quartic Surfaces

Introduction. It is well known that the plane sections of the Steiner Quartic Surface include all types to within projection of the rational plane quartic curve with simple singularities and that the invariants of any curve cut from this surface may be expressed as symmetric functions of the coefficients of the cutting plane.f If we vary this surface so that two of its double lines become coincident the plane sections are rational quartic curves with tacnodes; t if the three double lines are made coincident the resulting surface has as plane sections rational quartic curves with osenodes.? It is the purpose of this paper to express the invariants of the plane sections of these two surfaces in terms of the coefficients of the cutting plane.