Canonical class

In mathematics, the canonical bundle of a non-singular algebraic variety ${\displaystyle V}$ of dimension ${\displaystyle n}$ over a field is the line bundle ${\displaystyle \,\!\Omega ^{n}=\omega }$, which is the nth exterior power of the cotangent bundle Ω on V.

Over the complex numbers, it is the determinant bundle of holomorphic n-forms on V. This is the dualising object for Serre duality on V. It may equally well be considered as an invertible sheaf.

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