Translated by A. Maciocia, A. King and P. Kobak.
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).
Table of Contents
1. Exceptional collections, mutations and
helixes A. N. Rudakov
2. Construction of bundles on an elliptic curve
S. A. Kuleshov
3. Computing invariants of exceptional bundles
on a quadric S. K. Zube and D. Yu Nogin
4. Exceptional bundles of small rank on P1 x P1
D. Yu Nogin
5. On the functors Ext applied to exceptional
bundles on P2 A. I. Bondal and A. L. Gorodentsev
6. Homogeneous bundles A. I. Bondal and M. M.
7. Exceptional objects and mutations in derived
categories A. L. Gorodentsev
8. Helixes, representations of quivers and
Koszul algebras A. I. Bondal
9. Exceptional collections on ruled surfaces A.
V. Kvichansky and D. Yu Nogin
10. Exceptional bundles on K3 surfaces S. A.
11. Stability of exceptional bundles on three
dimensional projective space S. K. Zube
12. A symmetric helix on the Pluker quadric B.