Abstract
The aim of this note is to exhibit explicit sufficient cohomological criteria ensuring bigness of globally generated, rank-r vector bundles, \(r {\geqslant }2\), on smooth, projective varieties of even dimension \(d {\leqslant }4\). 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 fourfolds, etcetera.
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This research started during the visit of both authors at the Laboratoire de Mathématiques et Applications–Université de Poitiers; the authors thank this institution for the excellent hospitality and the friendly atmosphere. The collaboration has been partially supported by the Research Project “Families of curves: their moduli and their related varieties” (CUP: E81-18000100005)—Mission Sustainability—University of Rome Tor Vergata. Finally, the authors would like to thank the anonymous referee for carefully reading the manuscript, for his/her comments on the first version of this work (which have improved the exposition of the paper) and for valuable remarks inspiring Examples 3.1(e) and 4.1(b) of the present version.
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Bini, G., Flamini, F. Big Vector Bundles on Surfaces and Fourfolds. Mediterr. J. Math. 17, 17 (2020). https://doi.org/10.1007/s00009-019-1463-2
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DOI: https://doi.org/10.1007/s00009-019-1463-2