2019
DOI: 10.1515/advgeom-2018-0039
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Nef vector bundles on a quadric surface with the first Chern class (2, 1)

Abstract: We classify nef vector bundles on a projective space with first Chern class three over an algebraically closed field of characteristic zero; we see, in particular, that these nef vector bundles are globally generated if the second Chern class is less than eight, and that there exist nef but non-globally generated vector bundles with second Chern class eight and nine on a projective plane. 0 → O(−3) → O(−2) ⊕5 → O(−1) ⊕10 → O ⊕r+6 → E → 0; (9) c 2 = 5 and 0 → O(−1) ⊕2 → O(1) ⊕ O ⊕r+1 → E → 0; (10) c 2 = 5, n = … Show more

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Cited by 2 publications
(3 citation statements)
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“…Proof. The assertion was already proved in [33,27] if Q is non-singular. We attain a proof even if Q is singular.…”
Section: 3mentioning
confidence: 65%
See 2 more Smart Citations
“…Proof. The assertion was already proved in [33,27] if Q is non-singular. We attain a proof even if Q is singular.…”
Section: 3mentioning
confidence: 65%
“…By Lemma 3.10 (2), the cokernel of α| l : O(h)| l → F | l is locally free for general members l ∈ |f |. Then E is locally free in codimension 1 and hence torsion free by [27,Lemma 5.4]. Hence we have the following exact sequence:…”
Section: 3mentioning
confidence: 93%
See 1 more Smart Citation