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arXiv · 0804.0100

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

Edoardo Ballico·Francesco Malaspina
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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.

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BibTeXRIS

Edoardo Ballico, Francesco Malaspina. 2008-04-01. Vector Bundles on Products of Varieties with $n$-blocks Collections. https://arxiv.org/abs/0804.0100

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