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 d/dz_k. The antiholomorphic sections are spanned by d/dz^__k, of type (0, 1), where z^_ denotes the complex conjugate.
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