Computing limit linear series with infinitesimal methods

Laurent Evain

Displaying similar documents to “Computing limit linear series with infinitesimal methods”

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...

The Nash problem of arcs and the rational double points $D_{n}$

Camille Plénat (2008)

Annales de l’institut Fourier

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This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface $U$ with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points $D_{n}$ ( $n \geq 4$ ).

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of $d$ –actions (and the corresponding $d$ -dimensional Lie algebras) defined by commuting singular vector fields in $ℂ^{n}$ fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of $d$ vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

H.-Ch. Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont (2008)

Annales de l’institut Fourier

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Let $(V, 0)$ be a germ of a complete intersection variety in $ℂ^{n + k}$ , $n > 0$ , having an isolated singularity at $0$ and $X$ be the germ of a holomorphic vector field having an isolated zero at $0$ and tangent to $V$ . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of $X$ is also isolated in the ambient space $ℂ^{n + k}$ we give a formula for the homological index in terms of local linear algebra.

Essential dimension: A functorial point of view (after A. Merkurjev).

Berhuy, Grégory, Favi, Giordano (2003)

Documenta Mathematica

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Lech inequalities for deformations of singularities defined by power products of degree 2.

Richter, Tim (2002)

Beiträge zur Algebra und Geometrie

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Displaying similar documents to “Computing limit linear series with infinitesimal methods”

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

The Nash problem of arcs and the rational double points D n

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

Essential dimension: A functorial point of view (after A. Merkurjev).

Lech inequalities for deformations of singularities defined by power products of degree 2.

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

The Nash problem of arcs and the rational double points $D_{n}$