For a space with a notion of dimension and a notion of (Kähler) differential forms on it, the canonical bundle or canonical sheaf over is the line bundle (or its sheaf of sections) of -forms on , the -fold exterior product
of the bundle of 1-forms.
In particular the first Chern class of the canonical bundle on the 2-sphere is twice that of the basic line bundle on the 2-sphere, the generator in . See also at geometric quantization of the 2-sphere.
|line bundle||square root||choice corresponds to|
|canonical bundle||Theta characteristic||over Riemann surface and Hermitian manifold (e.g.Kähler manifold): spin structure|
|density bundle||half-density bundle|
|canonical bundle of Lagrangian submanifold||metalinear structure||metaplectic correction|
|determinant line bundle||Pfaffian line bundle|
|quadratic secondary intersection pairing||partition function of self-dual higher gauge theory||integral Wu structure|
In the context of algebraic geometry: