Vector Bundles on Products of Varieties with $n$-blocks Collections

Abstract

Here we consider the product of varieties with $n$-blocks collections . We give some cohomological splitting conditions for rank 2 bundles. A cohomological characterization for vector bundles is also provided. The tools are Beilinson's type spectral sequences generalized by Costa and Miró-Roig. Moreover we introduce a notion of Castelnuovo-Mumford regularity on a product of finitely many projective spaces and smooth quadric hypersurfaces in order to prove two splitting criteria for vector bundle with arbitrary rank.

15 pages, no figures

References in corpus (1)

• Qregularity and an Extension of Evans-Griffiths Criterion to Vector Bundles on Quadrics