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

Abstract

Let X ⊂ P r be a variety of almost minimal degree which is the projected image of a rational normal scroll X ̃ ⊂ P r + 1 from a point p outside of X ̃ . 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 ⊂ P r which contain X as a codimension one subvariety.