Maximal rank curves and singular points of the Hilbert scheme

Giorgio Bolondi; Jan O. Kleppe; Rosa Maria Miro-Roig

Displaying similar documents to “Maximal rank curves and singular points of the Hilbert scheme”

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.

The Lazarsfeld-Rao problem for Buchsbaum curves

Giorgio Bolondi, Juan C. Migliore (1989)

Rendiconti del Seminario Matematico della Università di Padova

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Curves on a double surface.

Scott Nollet, Enrico Schlesinger (2003)

Collectanea Mathematica

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Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes...

The Hilbert schemes of degree three curves

Scott Nollet (1997)

Annales scientifiques de l'École Normale Supérieure

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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...

Postulation and gonality for projective curves

Edoardo Ballico (1988)

Rendiconti del Seminario Matematico della Università di Padova

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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 ( $M_{v} \neq 0$ 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...

Weierstrass points and Weierstrass pairs on singular plane curves.

Ballico, E. (2000)

Mathematica Pannonica

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Some examples of Gorenstein liaison in codimension three.

Robin Hartshorne (2002)

Collectanea Mathematica

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Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension 2 in projective space. In this paper we study points in P3 and curves in P4 in an attempt to see how far typical codimension 2 results will extend. While the results are satisfactory for small degree, we find in each case examples where we cannot decide the outcome. This examples are candidates for counterexamples to the hoped-for extensions...