Beilinson Complex and Canonical Rings of Irregular Surfaces

An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P}^n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P}^n$ in terms of the vector bundles $\Omega_{\mathbb{P}^n}^j(j)$ for $0\le j\le n$. This title extends this theorem to weighted projective spaces.