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Holomorphic Differential Form

A holomorphic differential form of degree p on a complex manifold X is a bundle section of the bundle Omega_X^p whose coefficient functions in every coordinate chart are holomorphic functions. The bundle Omega_X^p consists of complex-valued differential k-forms with k=p. Such a section is also called a holomorphic p-form. In local holomorphic coordinates z_1, ..., z_n, it is a sum of terms

f_(i_1...i_p)(z)dz_(i_1) ^ ... ^ dz_(i_p),

where the coefficients f_(i_1...i_p) are holomorphic functions.

See also

Differential k-Form, Holomorphic Function, Hodge Number

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References

Voisin, C. Hodge Theory and Complex Algebraic Geometry I. Cambridge, England: Cambridge University Press, 2002.

Cite this as:

Weisstein, Eric W. "Holomorphic Differential Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HolomorphicDifferentialForm.html

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