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Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality for vector bundles and further, for coherent sheaves)

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Dualising sheaf of a nodal curve

Let $X$ be a projective nodal curve. Why is the dualizing sheaf of $X$ isomorphic to the log-cotangent bundle of $X$?
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