Boundary singularities of fundamental systems, flattenings of projective curves and Schubert cells

The paper studies the bifurcations of the flat points of projective curves and describes the singularities of the boundaries of the regions where typical three-parameter families of curves have no flat points. A flat-point-preserving transformation group of projective curves is introduced. Finite determinacy and versality theorems are proved for this group. A duality theorem is proved and some results concerning the connection of this problem with other problems of singularity theory are presented.