Does anyone know some interesting vector bundles on regular projective curves over finite fields that have constructive definitions? I am looking for interesting objects to toy with algorithmically (full disclosure, I'm looking for a neat example to put in a paper).
Ideally I would love a bundle that I can construct using combinations of line bundles, direct sums, tensor products and well chosen extensions. An example of that is Atiyah's construction of irreducible vector bundles on elliptic curves, but I'd love to find something in higher genus.
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