Helices and Vector Bundles: Seminaire Rudakov

doi:10.1017/CBO9780511721526

Helices and Vector Bundles

Seminaire Rudakov

This volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry. The work arises out of a series of seminars organised in Moscow by A. N. Rudakov. The first article sets up the general machinery, and later ones explore its use in various contexts. As to be expected, the approach is concrete; the theory is considered for quadrics, ruled surfaces, K3 surfaces and P3(C).

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Helices and Vector Bundles

Seminaire Rudakov

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Exceptional Collections, Mutations and Helixes
pp 1-6

Construction of Bundles on an Elliptic Curve
pp 7-22

Computing Invariants of Exceptional Bundles on a Quadric
pp 23-32

Exceptional Bundles of Small Rank on P1 × P1
pp 33-38

On the Functors Ext* Applied to Exceptional Bundles on P2
pp 39-44

Homogeneous Bundles
pp 45-56

Exceptional Objects and Mutations in Derived Categories
pp 57-74

Helixes, Representations of Quivers and Koszul Algebras
pp 75-96

Exceptional Collections on Ruled Surfaces
pp 97-104

Exceptional Bundles on K3 Surfaces
pp 105-114

Stability of Exceptional Bundles on Three Dimensional Projective Space
pp 115-118

A Symmetric Helix on the Plücker Quadric
pp 119-138

Index
pp 139-143

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Helices and Vector Bundles

Seminaire Rudakov

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