# Vector Bundles on P{sup 1}{sub ℤ} with Generic Fiber O ⊕ O(1) and Simple Jumps

## Abstract

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).

- Authors:

- St.Petersburg State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773933

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 232; Journal Issue: 5; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; CLASSIFICATION; VECTORS

### Citation Formats

```
Iakovenko, S. S., E-mail: sergey.s.yakovenko@gmail.com.
```*Vector Bundles on P{sup 1}{sub ℤ} with Generic Fiber O ⊕ O(1) and Simple Jumps*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3902-1.

```
Iakovenko, S. S., E-mail: sergey.s.yakovenko@gmail.com.
```*Vector Bundles on P{sup 1}{sub ℤ} with Generic Fiber O ⊕ O(1) and Simple Jumps*. United States. doi:10.1007/S10958-018-3902-1.

```
Iakovenko, S. S., E-mail: sergey.s.yakovenko@gmail.com. Wed .
"Vector Bundles on P{sup 1}{sub ℤ} with Generic Fiber O ⊕ O(1) and Simple Jumps". United States. doi:10.1007/S10958-018-3902-1.
```

```
@article{osti_22773933,
```

title = {Vector Bundles on P{sup 1}{sub ℤ} with Generic Fiber O ⊕ O(1) and Simple Jumps},

author = {Iakovenko, S. S., E-mail: sergey.s.yakovenko@gmail.com},

abstractNote = {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).},

doi = {10.1007/S10958-018-3902-1},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 232,

place = {United States},

year = {2018},

month = {8}

}

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