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.
