Geodesic
Bundles on $\mathbb{P}^1_\mathbb{Z}$ of rank $3$ and non-degenerate sections of bundles of rank $2$
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 135-146

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A classification of rank $3$ bundles with a trivial generic fiber and simple jumps is obtained. Using the resulting classification, it is proved that two bundles $E$ and $F$ of rank $2$ with a trivial generic fiber and simple jumps with equal discriminants are stably isomorphic, that is, $E\oplus\mathcal{O}\simeq F\oplus\mathcal{O}$. In the second part of the work it is shown that for a rank $2$ bundle with a trivial generic fiber there are non-degenerate sections of all degrees higher than minimal one. 
@article{ZNSL_2023_523_a7,
     author = {V. M. Polyakov},
     title = {Bundles on $\mathbb{P}^1_\mathbb{Z}$ of rank $3$ and non-degenerate sections of bundles of rank $2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--146},
     publisher = {mathdoc},
     volume = {523},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_523_a7/}
}
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V. M. Polyakov. Bundles on $\mathbb{P}^1_\mathbb{Z}$ of rank $3$ and non-degenerate sections of bundles of rank $2$. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 135-146. http://geodesic.mathdoc.fr/item/ZNSL_2023_523_a7/