On the Structure of Arithmetically Buchsbaum Curves in $\mathrm P^3_k$

Codimension one distributions of degree 2 on the three-dimensional projective space

“…Indeed, c 1 (N * G ) = −4, and To complete the proof, we must show that the sheaves described in display (9) do occur as conormal sheaves of foliation by curves. Recall that a null correlation sheaf P is defined as the cokernel of a morphism O P 3 (−1) → Ω 1 P 3 (1) given by a global section τ ∈ H 0 (Ω 1 P 3 (2)) that vanishes on a line L := (τ ) 0 . Dualizing the exact sequence…”

“…(1) T D is not µ-semistable if and only if c 2 (T D ) = −1; if that is the case (1,2) or (2,4); For all the other cases T D is µ-stable.…”

“…Let D be a codimension one distribution of degree 2 on P 3 . Then T D is µ-semistable whenever it does not split as a sum of line bundles; it can be strictly µ-semistable only when (c 2 (T D ), c 3 (T D )) = (1,2) or (2,4). In addition, c 1 (T D ) = 0, and the second and third Chern classes and spectra of T D are listed in Table 1, where Sing 1 (D) is given.…”

Biliaison classes of curves in 𝐏³

“…In this case we have s(C 0 ) = 2µ and ν(C 0 ) = 3µ + 1 (see e.g. [6]) and we get the Amasaki bound ν(C) ≤ s(C) + µ + 1 (see [1]). …”

Existence of homogeneous ideals fitting into long Bourbaki sequences

“…In particular, one can understand the numerical function θ X defined by Nollet in [13] from a structural point of view (see [7,Theorem 3.3]). When M is Buchsbaum, or equivalently, when the ring R/I is Buchsbaum, the relation ( * * ), together with the Borel fixedness of generic initial ideals, determines almost completely the basic sequences of the elements of I(M, p) (see [1,Sections 2 and 3], [2], [3, Sections 5 and 6]).…”