A NOETHER-LEFSCHETZ THEOREM FOR LINKED SURFACES IN P4

In this paper we consider surfaces X subset-of P4 linked to a smooth surface S subset-of P4, via a complete intersection of type (m1,m2). We use the theory of variations of Hodge structures to prove that the Picard group Pic(X) of general such X is generated by the hyperplane divisor H and the intersection curve C: = S intersection X, if the linking degrees m(i) are sufficiently large.