Given a holomorphic line bundle $L$ on a Riemann surface $M\,,$ with $L^2$ nontrivial, when is it true that the only holomorphic subbundles of $$L\oplus L^{-1}$$ are $L\oplus\{0\}$ and $\{0\}\oplus L^{-1}\,?$. I have seen things like this stated for genus $\ge 2$ but I'm not sure how to see that it is true.
2026-03-25 20:36:30.1774470990
Subbundles of Direct Sum of Holomorphic Line Bundles
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