Lectures on Vector Bundles

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Hardcover | 5 May 1997

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260 Pages

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22.86 x 15.24 x 1.91

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This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Industry Reviews

'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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Vector Bundles On Algebraic Curves
Generalities
The Riemann-Roch formula
Topological
The Hilbert scheme
Semi-stability
Invariant geometry
The construction of M(r,d)
Study of M(r,d)
Moduli Spaces Of Semi-Stable Sheaves On The Projective Plane
Introduction
Operations on semi-stable sheaves
Restriction to curves
Bogomolov's theorem
Bounded families
The construction of the moduli space
Differential study of the Shatz stratification
The conditions for existence
The irreducibility
The Picard group
Bibliography
Table of Contents provided by Publisher. All Rights Reserved.

Lectures on Vector Bundles

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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