Covers of algebraic varieties IV. A Bertini theorem for scandinavian covers

Let Y be an integral scheme and fix locally free C-y - sheaves epsilon A an d B of ranks 5, 3 and 3 respectively. Consider the projective bundle IP:= I P(epsilon) n --> Y and a morphism delta : Pi* A --> Pi* B(1) and let X := D -1(delta) be the locus of points x is an element of IP where rk(delta (x)) less than or equal to 1. Then the map rho := (Pi)\x :X --> Y is a cover of degree d = 6 if dim(X boolean AND Pi (-1) (y)) = 0 for each y is an element of Y. We call such a cover scandinavian. We prove a Bertini - type theorem and we give some examples of scandinavian and non scandinavian covers of d egree 6.