Complex Projective Geometry - Ellingsrud, G. / Peskine, C. / Sacchiero, G. / Stromme, S. A. (eds.)
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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? Such problems have often been reformulated over the last decade; often the need for a deeper analysis of the works of classical algebraic geometers was recognised. These…mehr

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Produktbeschreibung
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? Such problems have often been reformulated over the last decade; often the need for a deeper analysis of the works of classical algebraic geometers was recognised. These questions were addressed at successive conferences held in Trieste and Bergen. New results, work in progress, conjectures and modern accounts of classical ideas were presented. This collection represents a development of the work conducted at the conferences; the Editors have taken the opportunity to mould the papers into a cohesive volume.

Table of contents:
1. Speciality one rational surfaces in P4 J. Alexander; 2. Bounding sections of bundles on curves E. Arrondo and I. Sols; 3. The smooth surfaces of degree 9 in P4 A. B. Aure and K. Ranestad; 4. Compactifying the space of elliptic quartic curves D. Avritzer and I. Vainsencher; 5. Threefolds of degree 11 in P5 M. Beltrametti, M. Schneider and A. J. Sommese; 6. Complete extensions and their map to moduli space A. Bertram; 7. On the Betti numbers of the moduli space of stable bundles of rank two on a curve E. Bifet, F. Ghione and M. Letizia; 8. Gaussian maps for certain families of canonical curves C. Ciliberto and R. Miranda; 9. Geometry of the Horrocks bundle on P3 W. Decker, N. Manolache and F. O. Schreyer; 10. Stability and restrictions of Picard bundles, with an application to the normal bundles of elliptic curves L. Ein and R. Lazarsfeld; 11. Sections planes et majoration du genre des courbes gauches Ph. Ellia and R. Strano; 12. A tribute to Corrado Segre F. Ghione and G. Ottaviani; 13. Un aperçu des travaux mathématiques de G. H. Halphen (1844-1889) L. Gruson; 14. The source double-point cycle of a finite map of codimension one S. Kleiman; 15. Fibré déterminant et courbes de saut sur les surfaces algébriques J. Le Potier; 16. Courbes minimales dans les classes de biliaison M. Martin-Deschamps and D. Perrin; 17. Fano 3-folds S. Mukai; 18. Polarized K3 surfaces of genus 18 and 20 S. Mukai; 19. Projective compactifications of complex affine varieties S. Muller-Stach; 20. On generalized Laudal's lemma R. Strano; 21. Sur la stabilité des sous-variétés lagrangiennes des variétés symplectiques holomorphes C. Voisin; 22. Introduction to Gaussian maps on an algebraic curve J. Wahl; 23. Some examples of obstructed curves in P3 C. H. Walter.

New methods for tackling a variety of questions in algebraic geometry were addressed at successive conferences held in Trieste and Bergen. This collection represents a development of the work conducted at the conferences; the Editors have taken the opportunity to mould the papers into a cohesive volume.

A volume of papers describing new methods in algebraic geometry.
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