Big Vector Bundles on Surfaces and Fourfolds
Abstract
The aim of this note is to exhibit explicit sufficient criteria ensuring bigness of globally generated, rank-r vector bundles, r ≥slant 2, on smooth, projective varieties of even dimension d ≤slant 4. We also discuss connections of our general criteria to some recent results of other authors, as well as applications to tangent bundles of Fano varieties, to suitable Lazarsfeld-Mukai bundles on four-folds, etcetera.
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