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.

*This entry contributed by Todd
Rowland*

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## Cite this as:

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

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