In the book Complex Geometry - Huybrechts. The author says that the $k-$th wedge product of the holomorphic cotangent bundle $T^\ast X$ is the set of holomorphic $k-$forms. I know that an holomorphic $k-$ form is a section of the wedge product-bundle(WPB). Why the author calls a point of WPB "holomorphic form"?
Definition in Complex Geometry - Huybrechts
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definition
differential-forms
complex-geometry
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0That's not what the book says (at least not my edition). Definition 2.2.14 says "*The bundle of holomorphic $p$-forms is $\Omega_X^p:= \bigwedge^p\Omega_X$ [...]*" – 2017-01-21
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0Yes, but $\Omega_X$ is just the dual bundle of $TX$. – 2017-01-22
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0The point of my comment is that Huybrechts didn't write "the set of holomorphic k-forms". – 2017-01-22
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0Yes, but I think that "bundle" or "set" is the same in this contest. – 2017-01-22
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1I think that that is not correct. By "bundle of X" he means "bundle whose sections are X": Huybrechts often uses bundles and their spaces of sections interchangeably. – 2017-01-22