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 (z_1,...z_n), it is spanned by the nonvanishing section dz_1 ^ ... ^ dz_n. 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 nth exterior power of the dual bundle to the holomorphic tangent bundle.

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.

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