Holomorphic Tangent Bundle
The holomorphic tangent bundle to a complex manifold is given by its complexified tangent vectors which are of type (1,0). In a coordinate chart z=(z_1,...,z_n), the bundle is spanned by the local bundle sections partial/partialz_k. The antiholomorphic sections are spanned by partial/partialz^__k, of type (0,1), where z^_ denotes the complex conjugate.
See also
Complex Structure, Hermitian Metric, Holomorphic Line Bundle, Holomorphic Vector Bundle, Tangent BundleThis entry contributed by Todd Rowland
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Rowland, Todd. "Holomorphic Tangent Bundle." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HolomorphicTangentBundle.html