Geodesic
Vector bundles on $\mathbf P^1_\mathbb Z$ with generic fiber $\mathcal{O\oplus O}(1)$ and simple jumps
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 218-237

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We study vector bundles on the projective line over a Dedekind domain $A$. In the case where $A$ is a PID, we get a complete classification of rank 2 vector bundles with generic fiber $\mathcal{O\oplus O}(1)$ and with special fibers isomorphic either to $\mathcal{O\oplus O}(1)$ or $\mathcal O(-1)\oplus\mathcal O(2)$. 
@article{ZNSL_2016_452_a11,
     author = {S. S. Iakovenko},
     title = {Vector bundles on $\mathbf P^1_\mathbb Z$ with generic fiber $\mathcal{O\oplus O}(1)$ and simple jumps},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--237},
     publisher = {mathdoc},
     volume = {452},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a11/}
}
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S. S. Iakovenko. Vector bundles on $\mathbf P^1_\mathbb Z$ with generic fiber $\mathcal{O\oplus O}(1)$ and simple jumps. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 218-237. http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a11/