Chern classes and cohomology for rank 2 reflexive sheaves on P³

p-Buchsbaum rank 2 bundles on the projective space

“…Based on the evidence here presented and also motivated by results due to Roggero and Valabrega in [16], especially Propositions 5 and 6 and Theorem 2 there, we propose the following classification of 3-Buchsbaum rank 2 bundles on P 3 .…”

Classification of foliations by curves of low degree on the three-dimensional projective space

“…cannot be injective since h 0 (E) = 0 by the stability of E, thus contradicting the existence of the exact sequence in display (24).…”

“…P 3 ) ≥ 13, then there is a morphism ϕ : E(−3) → Ω 1 P 3 which does not factor through 2 • O P 3 (−2). By the second item in Lemma 6.10, we can choose this morphism to be injective; if coker ϕ is not torsion free, we would again get in contradiction with the existence of the sequence in display (24). Conversely, if h 0 (E ⊗ Ω 1 P 3 ) = 12, then every monomorphism ϕ : E(−3) → Ω 1…”

“…Let us first prove P has codimension one; indeed, let G be the kernel of the composed epimorphism Ω 1 P 3 → K → K/P . Using the Snake Lemma, we get a short exact sequence (24) 0 → E(−3)…”