In mathematics, the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle \,\! \Omega ^{n}=\omega } , which is the n {\displaystyle n} th exterior power of the cotangent bundle Ω {\displaystyle \Omega } on V {\displaystyle V} . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle T ∗ V {\displaystyle T^{*}V} .
In mathematics, the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle \,\! \Omega ^{n}=\omega } , which is the n {\displaystyle n} th exterior power of the cotangent bundle Ω {\displaystyle \Omega } on V {\displaystyle V} . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle T ∗ V {\displaystyle T^{*}V} .
Source: Wikipedia "Canonical bundle" · CC BY-SA 4.0
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