I refer to definition 1.3.3 on the text by David Huybrechts, where he stated that $\mathcal{A}_{\mathbb{C}}^k(U)$ and $\mathcal{A}^{p,q}(U)$ denote the spaces of sections of $\bigwedge^k_{\mathbb{C}}U$ and $\bigwedge^{p,q}_{\mathbb{C}}U$ respectively.
My question is what exactly are $\mathcal{A}_{\mathbb{C}}^k(U)$ and $\mathcal{A}^{p,q}(U)$? It is also stated that $\bigwedge^k_{\mathbb{C}}U$ and $\bigwedge^{p,q}_{\mathbb{C}}U$ are complex vector bundles but I have trouble seeing how this is so.
I would greatly appreciated if someone who has the book can explain it to me. Thanks!