ON VARIETIES OF ALMOST MINIMAL DEGREE II: A RANK-DEPTH FORMULA

Abstract

Let X subset of P(K)(r) denote a variety of almost minimal degree other than a normal del Pezzo variety. Then X is the projection of a rational normal scroll (X) over tilde subset of P(K)(r+1) from a point p is an element of P(K)(r+1)\(X) over tilde. We show that the arithmetic depth of X can be expressed in terms of the rank of the matrix M'(p), where M' is the matrix of linear forms whose 3 x 3 minors define the secant variety of (X) over tilde.