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  "body": "\n## Summary\n\nA stable vector bundle is a [[vector bundle|P4DZM975BV]] whose proper nonzero subbundles all have smaller slope than the bundle itself.\nThe slope of a bundle is its degree divided by its rank.\nStability is the condition that makes vector bundles on a curve form a good [[moduli space|FJZRW9P0K3]].\nIt was introduced by David Mumford in the setting of [[geometric invariant theory|9EG3A21ET1]].\nOver a compact Riemann surface, the Narasimhan–Seshadri theorem identifies stable bundles of degree $0$ with irreducible unitary representations of the fundamental group.\n\n## Explanations\n\n### L1 human\n\nA vector bundle on a curve has two numbers: its rank $r$ and its degree $d$, which measures how twisted it is.\nThe slope $d/r$ is the twist per dimension.\nThe bundle is stable when no smaller piece inside it is relatively more twisted than the whole.\nA direct sum $L_1 \\oplus L_2$ of line bundles with $\\deg L_1 \u003e \\deg L_2$ is not stable, because $L_1$ is a piece with larger slope.\nStable bundles have only scalar automorphisms, which is why they can be classified by a well-behaved space.\n",
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