Vector bundles E on P-3 with homological dimension 2 and chi(End E)=1

摘要

We find the complete integer solutions of the equation X-2 + Y-2 + Z(2) - 4XY - 4YZ + 10XZ = 1. As an application, we prove that, for each solution (a, b, c) such that a > 0, b - 2a > 0 and (b - 2a)(2) >= 4a, there is a vector bundle E on P-3 defined by a minimal linear resolution 0 -> O-P3 (-2)(a) -> O-P3 (-1)(b) -> O-P3(c) -> E -> 0. In particular, E satisfies chi(End E) = 1.