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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 set of minimal...

The Hilbert scheme of space curves of small diameter

Jan Oddvar Kleppe (2006)

Annales de l’institut Fourier

This paper studies space curves $C$ of degree $d$ and arithmetic genus $g$ , with homogeneous ideal $I$ and Rao module $M = H_{*}^{1} (\tilde{I})$ , whose main results deal with curves which satisfy $_{0} {Ext}_{R}^{2} (M, M) = 0$ (e.g. of diameter, $diam M \leq 2$ ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, $H (d, g)$ , at $(C)$ under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of $C$ turns out to be equivalent to the...

The Hilbert schemes of degree three curves

Scott Nollet (1997)

Annales scientifiques de l'École Normale Supérieure

The Hilbert-Chow morphism and the incidence divisor.

Ross, Joseph (2011)

Documenta Mathematica

The moduli space of commutative algebras of finite rank

Bjorn Poonen (2008)

Journal of the European Mathematical Society

The moduli space of rank- $n$ commutative algebras equipped with an ordered basis is an affine scheme $𝔅_{n}$ of finite type over $ℤ$ , with geometrically connected fibers. It is smooth if and only if $n \leq 3$ . It is reducible if $n \geq 8$ (and the converse holds, at least if we remove the fibers above $2$ and $3$ ). The relative dimension of $𝔅_{n}$ is $\frac{2}{27} n^{3} + O (n^{8 / 3})$ . The subscheme parameterizing étale algebras is isomorphic to ${GL}_{n} / S_{n}$ , which is of dimension only $n^{2}$ . For $n \geq 8$ , there exist algebras that are not limits of étale algebras. The dimension calculations...

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Techniques de construction et théorèmes d'existence en géométrie algébrique IV : les schémas de Hilbert

The Betti numbers of the Hilbert scheme of ponts on a smooth projective surface.

The Chow rings of smooth complete $SL (2)$ -embeddings

The cohomology ring of the Hilbert scheme of 3 points on a smooth projective variety.

The coniveau filtration and non-divisibility for algebraic cycles.

The decomposition and specialization of algebraic families of vector bundles

The dimension of the Chow variety of curves

The Euler series of restricted Chow varieties

The Hilbert Function of curves on certain smooth quartic surfaces.

The Hilbert Scheme of Buchsbaum space curves

The Hilbert scheme of space curves of small diameter

The Hilbert schemes of degree three curves

The Hilbert-Chow morphism and the incidence divisor.

The moduli space of commutative algebras of finite rank

The Number of Twisted Cubic Curves on the General Quintic Threefold.

The push-forward and Todd class of flag bundles

Théorème de Riemann-Roch par désingularisation

Torsion algebraic cycles and a theorem of Roitman

Torsion in CH2 of Severi-Brauer varieties and indecomposability of generic algebras.

Torsion in K2 of fields and 0-cycles on rational surfaces.

Currently displaying 1 – 20 of 24