On globally generated vector bundles on projective spaces II

Abstract

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

Geometry of the Sasakura bundle

“…This last section aims to describe the place of the Sasakura bundle in this context, following the joint paper with Coanda and Manolache [2]. Chronologically, the main contributions in this area are: -Chiodera and Ellia [8] in ('12) determined the Chern classes of rank 2 globally generated vector bundles with c 1 ≤ 5 on P n , -Sierra and Ugaglia [14] in ('09) classified globally generated vector bundles with c 1 ≤ 2 on P n , -Sierra and Ugaglia [15] in ('14) and independently Manolache with the author [3] in ('13) classified globally generated vector bundles with c 1 ≤ 3 on P n , -Coanda, Manolache and the author [2] ('13) classified globally generated vector bundles with c 1 ≤ 4 on P n .…”

Nef vector bundles on a quadric surface with the first Chern class (2, 1)

“…Hence the composite of d 2 and the projection O(−2) ⊕3r+3 ⊕ O(−3) → O(−3) is non-zero and thus a surjection. Therefore the resolution above is reduced to that in case (17) of Theorem 1. This completes the proof of Theorem 1 for the case n = 2, c 2 = 9, and h 0 (E) = 0.…”

“…Anghel-Manolache [1] and Sierra-Ugaglia [17] classified globally generated vector bundles on a projective space with first Chern class three. Since global generation implies nefness, Theorem 1 is a generalization of their results.…”

On Higher Rank Globally Generated Vector Bundles over a Smooth Quadric Threefold

“…In [16] the second author carried out the case of rank two with c 1 = 3 on P 3 and in [7] the authors continued the study until c 1 ≤ 5. This classification was extended to any rank in [17] and to any P n (n ≥ 3) in [2] and [23]. In [9] are shown the possible Chern classes of rank two globally generated vector bundles on P 2 .…”