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, $r⩾2$, on smooth, projective varieties of even dimension $d⩽4$. 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.

14 pages; to appear in Mediterranean Journal of Mathematics; research started during visit at Lab. Math. Appl--U. Poitiers and supported by the Res. Proj. "Families of curves"(CUP: E81-18000100005) - Univ. Rome Tor Vergata. Thanks to the anonymous referee for carefully reading the manuscript and for valuable remarks inspiring examples in this new version