Canonical Bundle

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart , it is spanned by the nonvanishing section . The transition function between coordinate charts is given by the determinant of the Jacobian of the coordinate change.

The canonical bundle is defined in a similar way to the holomorphic tangent bundle. In fact, it is the th exterior power of the dual bundle to the holomorphic tangent bundle.