a b s t r a c tA classification is given for globally generated vector bundles E of rank k on P n having first Chern class c 1 (E) = 2. In particular, we get that they split if k < n unless E is a twisted null-correlation bundle on P 3 . In view of the well-known correspondence between globally generated vector bundles and maps to Grassmannians, we obtain, as a corollary, a classification of double Veronese embeddings of P n into a Grassmannian G(k − 1, N) of (k − 1)-planes in P N .

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Extending a previous result of the authors, we classify globally generated vector bundles on projective spaces with first Chern class equal to three.Comment: To appear in J. Pure Appl. Algebr