Complex Projective Geometry: Selected Papers

Algebraic geometers have renewed their interest in the interplay between algebraic vector bundles and projective embeddings. New methods have been developed for questions such as: What is the geometric content of syzygies and of bundles derived from them? How can they be used for giving good compactifications of natural families? Which differential techniques are needed for the study of families of projective varieties? These questions are addressed in this cohesive volume, where results, work in progress, conjectures, and modern accounts of classical ideas are presented. Cover......Page 1 Series Titles......Page 2 Title Page......Page 4 Copyright Page......Page 5 Contents......Page 6 Introduction......Page 8 List of Talks of Projective Varieties......Page 9 List of Talks of Vector Bundles ........Page 10 List of Participants......Page 11 Speciality one rational surfaces in P^4......Page 12 Bounding sections of bundles on curves......Page 35 The smooth surfaces of degree 9 in P4......Page 43 Compactifying the space of elliptic quartic curves......Page 58 Threefolds of degree 11 in P^5......Page 70 Complete extensions and their map to moduli space......Page 92 On the Betti numbers of the moduli space of stable bundles of rank two on a curve......Page 103 Gaussian maps for certain families of canonical curves......Page 117 Geometry of the Horrocks bundle on P3......Page 139 Stability and restrictions ofPicard bundles, with an application to the normal bundles of elliptic curves......Page 160 Sections planes et majoration du genre des courbes gauches......Page 168 A tribute to Corrado Segre......Page 186 Un apergu des travaux mathtmatiques de GB. Halphen (1844-1889)......Page 200 The source double-point cycle of a finite map of codimension one......Page 210 Fibre determinant et courbes de saut sur les surfaces algibriques......Page 224 Courbes minimales dans les classes de biliaison......Page 252 Fano3-folds......Page 266 Polarized K3 surfaces of genus 18 and 20......Page 275 Protective compactifications of complex afflne varieties 2......Page 88 On generalized Laudal's lemma......Page 295 Sur la stability des sous-varies lagrangiennes des variitis symplectiques holomorphes......Page 305 Introduction to Gaussian maps on an algebraic curve......Page 315 Some examples of obstructed curves in P^3......Page 335