examples of derived categories

\(\mathbf{D}^b {{\mathsf{Coh}}{\mathbf{C}}^{\times}} = \left\langle{{\mathcal{O}}_{{\mathbf{C}}^{\times}}}\right\rangle\)
- \(\mathbf{D}^b {{\mathsf{Coh}}{\mathbf{CP}}^2} = \left\langle{{\mathcal{O}}_{{\mathbf{CP}}^2}, {\mathcal{O}}_{{\mathbf{CP}}^2}(-1), {\mathcal{O}}_{{\mathbf{CP}}^2}(-2) }\right\rangle\)