UNE COURBE PLANE à NŒUDS ET à CUSPS OBSTRUéE Dé DEGRE PLUS BAS QUE LES EXEMPLES CONNUS.

J. Wahl proved the existence of a scheme H parametrizing the plane curves of fixed degree having some fixed numbers of nodes and cusps as its only singularities. Wahl builts from Mumford's example, a family of plane curves with nodes and cusps whose general member is a singular point of the scheme H but smooth in the reduced scheme H_red. Using the same method as Wahl, S. Guffroy builts a family of plane curves with nodes and cusps whose general member is a singular point of the scheme H and singular in the reduced scheme H_red. In this work, we construct, like Guffroy, from Sernesi's example, a family of plane curves with nodes and cusps of lower degree than those of Wahl or Guffroy. This result is the best known and the singularity is different from that appearing in Wahl or Guffroy. [ABSTRACT FROM AUTHOR]