Towards a structure theory for projective varieties of degree = codimension + 2

AbstractThe problem under consideration in this paper is that of finding a structure theory for varieties X of Pnk (k is an algebraically closed field of arbitrary characteristic) with degree (X) = codimension(X) + 2. Takao Fujita has a satisfactory classification theory for projective varieties of Δ-genus zero and one. In either case the singularities of X turn out to be of very special type. Our approach also sheds some light on the structure of these singularities