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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

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 $C$ , i.e. 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 (i.e. $N_{ℓ / V} ≃ {𝒪_{ℙ^{1}}}^{\oplus 2}$ ). 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...

On a Result of Riemenschneider.

Henry Pinkham (1975)

Manuscripta mathematica

On base change theorem and coherence in rigid cohomology.

Tsuzuki, Nobuo (2003)

Documenta Mathematica

On Border Basis and Gröbner Basis Schemes.

Lorenzo Robbiano (2009)

Collectanea Mathematica

On Deformations of Quintic Surfaces.

Eiji Horikawa (1976)

Inventiones mathematicae

On Deformations of Threedimensional Rational Manifolds.

Klaus Timmerscheidt (1981)

Mathematische Annalen

On Elliptic Surfaces in Characteristic p.

Kenji Ueno, Toshiyuki Katsura (1985)

Mathematische Annalen

On Families of Birationally Equivalent Varieties.

A. Bialynicki-Birula (1973)

Mathematische Annalen

On joint moduli spaces.

Liaw Huang (1995)

Mathematische Annalen

On limiting rational curves.

Xian Wu (1994)

Manuscripta mathematica

On moduli of algebraic varieties III. Fine moduli spaces

Herbert Popp (1975)

Compositio Mathematica

On Pencils of Curves and Deformations of Minimally Elliptic Singularities .

Ulrich Karras (1980)

Mathematische Annalen

On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

Here we give several examples of projective degenerations of subvarieties of $ℙ^{t}$ . The more important case considered here is the d-ple Veronese embedding of $ℙ^{n}$ ; we will show how to degenerate it to the union of $d^{n}$ n-dimensional linear subspaces of $ℙ^{t}; t : = (n + d) / (n! d!) - 1$ and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to postulation...

Currently displaying 1 – 20 of 23

Page 1 Next

Displaying 1 – 20 of 23

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

On a Result of Riemenschneider.

On base change theorem and coherence in rigid cohomology.

On Border Basis and Gröbner Basis Schemes.

On Deformations of Quintic Surfaces.

On Deformations of Threedimensional Rational Manifolds.

On Elliptic Surfaces in Characteristic p.

On Families of Birationally Equivalent Varieties.

On joint moduli spaces.

On limiting rational curves.

On moduli of algebraic varieties III. Fine moduli spaces

On Pencils of Curves and Deformations of Minimally Elliptic Singularities .

On projective degenerations of Veronese spaces

On the deformation of orthogonal bundles over the projective line.

On the deformation theory of structure constants for associative algebras.

On the Existence of Analytic Contractions.

On the geometry of quadrics and their degenerations.

On the homotopy of the complement to plane algebraic curves.

On the Infinitesimal Torelli Theorem for Certain irregular Surfaces of General Type.

On the Monodromy Group of Plane Curve Singularities.

Currently displaying 1 – 20 of 23