The Hilbert scheme of space curves of small diameter

Jan Oddvar Kleppe

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Displaying similar documents to “The Hilbert scheme of space curves of small diameter”

Obstructions to deforming curves on a $3$ -fold, II: Deformations of degenerate curves on a del Pezzo $3$ -fold

Hirokazu Nasu (2010)

Annales de l’institut Fourier

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We study the Hilbert scheme ${Hilb}^{s c} V$ of smooth connected curves on a smooth del Pezzo $3$ -fold $V$ . We prove that any degenerate curve $C$ , any curve $C$ contained in a smooth hyperplane section $S$ of $V$ , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) $χ (V, ℐ_{C} (S)) \geq 1$ and (ii) for every line $ℓ$ on $S$ such that $ℓ \cap C = \emptyset$ , the normal bundle $N_{ℓ / V}$ is trivial ( $N_{ℓ / V} ≃ {𝒪_{ℙ^{1}}}^{\oplus 2}$ ). As a consequence, we prove an analogue (for ${Hilb}^{s c} V$ ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...

Computing limit linear series with infinitesimal methods

Laurent Evain (2007)

Annales de l’institut Fourier

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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor. Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined...

The Drinfeld Modular Jacobian $J_{1} (n)$ has connected fibers

Sreekar M. Shastry (2007)

Annales de l’institut Fourier

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We study the integral model of the Drinfeld modular curve $X_{1} (n)$ for a prime $n \in 𝔽_{q} [T]$ . A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod $n$ . A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order $n$ in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of $X_{1} (n)$ which, after contractions...

Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$ -space

Robin Hartshorne, Irene Sabadini, Enrico Schlesinger (2008)

Annales de l’institut Fourier

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We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of $ℙ^{N}$ is glicci, that is, whether every zero-scheme in $ℙ^{3}$ is glicci. We show that a general set of $n \geq 56$ points in $ℙ^{3}$ admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in $ℙ^{3}$ .

Hereditary endomorphism rings of mixed Abelian groups.

Krylov, P.A. (2002)

Sibirskij Matematicheskij Zhurnal

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Extensions of semimodules and the Takahashi functor ${Ext}_{Λ} (C, A)$ .

Patchkoria, Alex (2003)

Homology, Homotopy and Applications

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Displaying similar documents to “The Hilbert scheme of space curves of small diameter”

Obstructions to deforming curves on a 3 -fold, II: Deformations of degenerate curves on a del Pezzo 3 -fold

Computing limit linear series with infinitesimal methods

The Drinfeld Modular Jacobian J 1 ( n ) has connected fibers

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Hereditary endomorphism rings of mixed Abelian groups.

Extensions of semimodules and the Takahashi functor Ext Λ ( C , A ) .

Obstructions to deforming curves on a $3$ -fold, II: Deformations of degenerate curves on a del Pezzo $3$ -fold

The Drinfeld Modular Jacobian $J_{1} (n)$ has connected fibers

Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$ -space

Extensions of semimodules and the Takahashi functor ${Ext}_{Λ} (C, A)$ .