Cohomological characterization of vector bundles on multiprojective spaces

We show that Horrocks criterion for the splitting of vector bundles on Pn can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool we use the theory of n-blocks and Beilinson type spectral sequences. Cohomological characterizations of vector bundles are also showed.