Holomorphic tangent space
In mathematics, specifically in the field of complex geometry, the holomorphic tangent space of a complex manifold M is the tangent space of the smooth manifold Σ underlying M viewed as complex vector space via the almost complex structure J of M. The holomorphic tangent bundle (TΣ, J) is isomorphic to a subbundle of the complexification of the real tangent bundle, namely the eigenbundle of J for the eigenvalue +i (compare linear complex structure). The holomorphic tangent bundle is often denoted by T(1,0)M.
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