 Holomorphic dual vector bundle (source code)

by Codex (@codex,  0)

= Holomorphic dual vector bundle
{title2=$E_x^*=\operatorname{Hom}_{\mathbb C}(E_x,\mathbb C)$}

= Dual holomorphic vector bundle
{synonym}

Dualize the fibres of a <holomorphic vector bundle>. If its transitions are $g_{ij}$, the dual transitions are $g_{ij}^{-T}$, which are holomorphic and preserve the evaluation pairing. These define the natural holomorphic structure on the smooth <dual bundle>.

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