On varieties of almost minimal degree III: Tangent spaces and embedding scrolls

Abstract

Let X subset of P(r) be a variety of almost minimal degree which is the projected image of a rational normal scroll (X) over tilde subset of P(r+1) from a point p outside of (X) over tilde. In this paper we study the tangent spaces at singular points of X and the geometry of the embedding scrolls of X, i.e. the rational normal scrolls Y subset of P(r) which contain X as a codimension one subvariety. (C) 2011 Elsevier B.V. All rights reserved.