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.
This entry contributed by Todd Rowland
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Rowland, Todd. "Canonical Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CanonicalBundle.html