Vector Bundles on P1ℤ with Generic Fiber O ⊕ O(1) and Simple Jumps

Resumo

Vector bundles on the projective line over a Dedekind domain A are studied. In the case where A is a principal ideal domain, a complete classification is obtained for rank 2 vector bundles with generic fiber O ⊕ O(1) and special fibers isomorphic either to O ⊕ O(1) or to O(−1) ⊕ O(2).