T a b l e of C o n t e n t s

Introduction page v I j

Part I : A brief survey of Noether-Lefschetz

problems

§ 1 The Noether-Lefschetz theorem 1

§ 2 Components of the Noether-Lefschetz locus 6

§ 3 Higher dimensional problems 9

Part II : The Picard group of a general surface

containing a space curve

S 1 Introduction 13

§ 2 Some classical facts 15

§ 3 The results 26

Part III : The Picard group of some general surfaces in P

r

§ 1 Introduction 57

§ 2 The generalization of Theorem II.3.1 in Pn*2 58

§ 3 The Picard group of general residual surfaces

in

P4

65

til