Displaying similar documents to “On the graded Betti numbers for large finite subsets of curves”

The Hilbert Scheme of Buchsbaum space curves

Jan O. Kleppe (2012)

Annales de l’institut Fourier

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We consider the Hilbert scheme H ( d , g ) of space curves C with homogeneous ideal I ( C ) : = H * 0 ( ℐ C ) and Rao module M : = H * 1 ( ℐ C ) . By taking suitable generizations (deformations to a more general curve) C ′ of C , we simplify the minimal free resolution of I ( C ) by e.g making consecutive free summands (ghost-terms) disappear in a free resolution of I ( C ′ ) . Using this for Buchsbaum curves of diameter one ( M v ≠ 0 for only one v ), we establish a one-to-one correspondence between the set 𝒮 of irreducible components of H ( d , g ) that contain ( C ) and a...

Non-obstructed subcanonical space curves.

Rosa M. Miró-Roig (1992)

Publicacions Matemàtiques

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Recall that a closed subscheme X ⊂ P is non-obstructed if the corresponding point x of the Hilbert scheme is non-singular. A geometric characterization of non-obstructedness is not known even for smooth space curves. The goal of this work is to prove that subcanonical k-Buchsbaum, k ≤ 2, space curves are non-obstructed. As a main tool we use Serre's correspondence between subcanonical curves and vector bundles.

Gorenstein liaison of some curves in P.

Joshua Lesperance (2001)

Collectanea Mathematica

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Despite the recent advances made in Gorenstein liaison, there are still many open questions for the theory in codimension ≥ 3. In particular we consider the following question: given two curves in P with isomorphic deficiency modules (up to shift), can they be evenly Gorenstein linked? The answer for this is yes for curves in P, due to Rao, but for higher codimension the answer is not known. This paper will look at large classes of curves in P with isomorphic deficiency modules and show...