Joseph Le Potier, J. Le Potier, Le Potier J

Lectures on Vector Bundles

• Gebundenes Buch

Produktbeschreibung

This work consists of two courses on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The construction and elementary properties of the moduli spaces of stable bundles are also discussed. In particular, Hilbert-Grothendieck schemes of vector bundles are constructed, and Mumford's geometric invariant theory is succinctly treated. The second part centres on the structure of the moduli space of semi-stable sheaves on the projective plane. Existence conditions for sheaves of given rank and Chern Class and construction ideas are sketched in the general context of projective algebraic surfaces. Professor Le Potier has provided a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Table of contents:
Part I. Vector Bundles On Algebraic Curves: 1. Generalities; 2. The Riemann-Roch formula; 3. Topological; 4. The Hilbert scheme; 5. Semi-stability; 6. Invariant geometry; 7. The construction of M(r,d); 8. Study of M(r,d); Part II. Moduli Spaces Of Semi-Stable Sheaves On The Projective Plane; 9. Introduction; 10. Operations on semi-stable sheaves; 11. Restriction to curves; 12. Bogomolov's theorem; 13. Bounded families; 14. The construction of the moduli space; 15. Differential study of the Shatz stratification; 16. The conditions for existence; 17. The irreducibility; 18. The Picard group; Bibliography.

This work consists of two courses on the moduli spaces of vector bundles. The first is introductory, and assumes very little background; the second is more advanced and takes the reader into current areas of research. This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 260
• Erscheinungstermin: 20. Dezember 2004
• Englisch
• Abmessung: 235mm x 157mm x 20mm
• Gewicht: 577g
• ISBN-13: 9780521481823
• ISBN-10: 0521481821
• Artikelnr.: 22184848

Inhaltsangabe

Part I. Vector Bundles On Algebraic Curves: 1. Generalities
2. The Riemann-Roch formula
3. Topological
4. The Hilbert scheme
5. Semi-stability
6. Invariant geometry
7. The construction of M(r,d)
8. Study of M(r,d)
Part II. Moduli Spaces Of Semi-Stable Sheaves On The Projective Plane
9. Introduction
10. Operations on semi-stable sheaves
11. Restriction to curves
12. Bogomolov's theorem
13. Bounded families
14. The construction of the moduli space
15. Differential study of the Shatz stratification
16. The conditions for existence
17. The irreducibility
18. The Picard group
Bibliography.