In the recent years, one has seen the developements of new methods in the study of projective complex varieties. Among others, techniques involving algebraic vector bundles and deformation theory have had an increasingly important role. Surprisingly or not, these developements often stem from problems in traditional Projective Geometry. They were therefore followed by a renewed interest in the works and ideas of the old masters of the subject.

These new trends were studied during two conferences organized, in collaboration, by the Universities of Trieste (“Projective Varieties”, 19–24 June 1989) and Bergen (“Vector Bundles and Special Projective Embeddings”, 3–16 July 1989). We publish here selected papers from these meetings, hoping they will reflect the main subjects of interest as well as the pleasant working atmosphere of this month of Projective Complex Geometry.

Acknowledgements.

The conference “Projective Varieties” in Trieste was made possible by the supports of the “Consiglio Nazionale delle Ricerche” (C.N.R.), the regional authorities of “Friuli-Venezia Giulia” and the University of Trieste.

The conference “Vector Bundles and Special Projective Embeddings” in Bergen was made possible by the support of the Norwegian Research Council for Sciences and Humanities' (N.A.V.F.). The support given by the French authorities through “le Conseiller Scientifique” at the French Embassy in Norway allowed for a particularly important French participation. The University in Bergen provided an excellent working environment.