Algebraic Geometry

The question of how the geometry of a projective variety is determined by its hyperplane sections has been an attractive area of algebraic geometry for at least a century. A century ago Picard's study of hyperplane sections led him to his famous theorem on the 'regularity of the adjoint '. This result, which is the Kodaira vanishing theorem in the special case of very ample line bundles on smooth surfaces, has led to many developments to this day. Castelnuovo and Enrique? related the first Betti number of a variety and its hyperplane section. This and Picard's work led to the Lefschetz hyperplane section theorem and the modern work on ampleness and connectivity. A large part of the study of hyperplane sections has always been connected with the classification of projective varieties by projective invariants. Recent new methods, such as the adjunction mappings developed to study hyperplane sections, have led to beautiful general results in this classification. The papers in this proceedings of the L'Aquila Conference capture this lively diversity. They will give the reader a good picture of the currently active parts of the field.The papers can only hint at the friendly 'give and take' that punctuated many talks and at the mathematics actively discussed during the conference.
The success of this conference was in large part due to the Scientific and Organizing Committe: Professor Mauro Beltrametti (Genova), Professor Aldo Biancofiore L'Aquila), Professor Antonio Lanteri (Milano), and Professor Elvira Laura Livorni (L'Aquila). The publication of this proceedings would not have been possible except for the efforts of
Professor E.L.Livorni.