Number of singular points of an annulus in $\mathbb{C}^2$

Maciej Borodzik; Henryk Zołądek

Displaying similar documents to “Number of singular points of an annulus in $ℂ^{2}$ ”

Exceptional singular $ℚ$ -homology planes

Karol Palka (2011)

Annales de l’institut Fourier

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We consider singular $ℚ$ -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is $ℂ^{1}$ - or $ℂ^{*}$ -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type $A_{1}$ and $A_{2}$ respectively.

Weierstrass gaps and curves on a scroll.

Carvalho, Cícero (2002)

Beiträge zur Algebra und Geometrie

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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

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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...

When singular points determine quadratic systems.

Artes, Joan C., Llibre, Jaume, Vulpe, Nicolae (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Moduli spaces for linear differential equations and the Painlevé equations

Marius van der Put, Masa-Hiko Saito (2009)

Annales de l’institut Fourier

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A systematic construction of isomonodromic families of connections of rank two on the Riemann sphere is obtained by considering the analytic Riemann–Hilbert map $R H : ℳ \to ℛ$ , where $ℳ$ is a moduli space of connections and $ℛ$ , , is a moduli space for analytic data (, ordinary monodromy, Stokes matrices and links). The assumption that the fibres of $R H$ (, the isomonodromic families) have dimension one, leads to ten moduli spaces $ℳ$ . The induced Painlevé equations are computed explicitly. Except for the...

Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation

Serge Cantat, Frank Loray (2009)

Annales de l’institut Fourier

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We consider representations of the fundamental group of the four punctured sphere into $SL (2, ℂ)$ . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from $SU (2)$ -representations. We prove the absence of invariant affine structure...

Decompositions of hypersurface singularities oftype $J_{k, 0}$

Piotr Jaworski (1994)

Annales Polonici Mathematici

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Applications of singularity theory give rise to many questions concerning deformations of singularities. Unfortunately, satisfactory answers are known only for simple singularities and partially for unimodal ones. The aim of this paper is to give some insight into decompositions of multi-modal singularities with unimodal leading part. We investigate the $J_{k, 0}$ singularities which have modality k - 1 but the quasihomogeneous part of their normal form only depends on one modulus.

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...

Displaying similar documents to “Number of singular points of an annulus in ℂ 2 ”

Displaying similar documents to “Number of singular points of an annulus in $ℂ^{2}$ ”