Helices and Vector Bundles
Seminaire Rudakov

A. N. Rudakov (Edited by)

9780521388115, Cambridge University Press

Paperback, published 12 July 1990

152 pages
22.8 x 15.2 x 0.9 cm, 0.232 kg

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).

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. Kapranov
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. Kuleshov
11. Stability of exceptional bundles on three dimensional projective space S. K. Zube
12. A symmetric helix on the Pluker quadric B. V. Karpov.

Subject Areas: Algebraic geometry [PBMW]