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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.Read more
- Author is world class authority on subject
- Book arises from courses given in Paris
- Second part takes reader into current areas of research
Reviews & endorsements
'The whole book is well written and is a valuable addition to the literature … It is essential purchase for all libraries maintaining a collection in algebraic geometry, and strongly recommended for individual researchers and graduate students with an interest in vector bundles.' Peter Newstead, Bulletin of the London Mathematical Society
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- Date Published: March 1997
- format: Hardback
- isbn: 9780521481823
- length: 260 pages
- dimensions: 236 x 157 x 19 mm
- weight: 0.477kg
- contains: 1 b/w illus.
- availability: Available
Table of Contents
Part I. Vector Bundles On Algebraic Curves:
2. The Riemann-Roch formula
4. The Hilbert scheme
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
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
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