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Equimultiple deformations of isolated singularities
Israel Journal of Mathematics, 2001The paper is devoted to the deformation theory of isolated hypersurface singularities over the complexes or reals. A deformation of a germ \(f\) is versal if it contains all possible singularities close to \(f\), modulo an equivalence relation on singularities. The authors study versal deformations with respect to different equivalences. In particular,
Scherback, I., Shustin, E.
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Exceptional Deformations of Quadrilateral Singularities and Singular K3 Surfaces
Bulletin of the London Mathematical Society, 1987It was shown by Pham in 1970 (unpublished) that the singularity \(y^3+ayx^6+x^9=0\) deforms to \(E_6+E_8\) only if the parameter \(a\) vanishes. By Looijenga's general theory [\textit{E. Looijenga}, Math. Ann. 269, 357--387 (1984; Zbl 0568.14003)] such a deformation corresponds to a \(K3\) surface containing a certain configuration of curves.
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Free deformations of hypersurface singularities
Journal of Mathematical Sciences, 2011The article is devoted to the study of the classification problem for Saito free divisors making use of the deformation theory of varieties. In particular, in the quasihomogeneous case, we describe an approach for computation of free deformations of quasicones over quasismooth varieties based on properties of deformations of varieties with \( {\mathbb ...
A. G. Aleksandrov, J. Sekiguchi
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ISOMONODROMY DEFORMATIONS OF EQUATIONS WITH IRREGULAR SINGULARITIES
Mathematics of the USSR-Sbornik, 1992See the review Zbl 0717.34011.
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Deformations of Surface Singularities
2013Altmann, K. and Kastner, L.: Negative Deformations of Toric Singularities that are Smooth in Codimension Two.- Bhupal, M. and Stipsicz, A.I.: Smoothing of Singularities and Symplectic Topology.- Ilten, N.O.: Calculating Milnor Numbers and Versal Component Dimensions from P-Resolution Fans.- Nemethi, A: Some Meeting Points of Singularity Theory and Low ...
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NON-NEGATIVE DEFORMATIONS OF WEIGHTED HOMOGENEOUS SINGULARITIES
Glasgow Mathematical Journal, 2017AbstractWe consider a weighted homogeneous germ of complex analytic variety (X, 0) ⊂ (ℂn, 0) and a function germ f : (ℂn, 0) → (ℂ, 0). We derive necessary and sufficient conditions for some deformations to have non-negative degree (i.e., for any additional term in the deformation, the weighted degree is not smaller) in terms of an adapted version of ...
Nuño-Ballesteros, J. J. +2 more
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Deformation of Singularities Via Quivers
2000McKay linked together binary polyhedral groups and the extended CDW - diagrams. A geometric explanation for this phenomenon was given by Artin and Gonzales - Sprinberg, Artin and Verdier, and Esnault. Ebeling, Slodowy [8] and Cassens [2] constructed the versal deformation in terms of representations of the quivers in case of Kleinian singularity ...
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Equisingular Deformations of Normal Surface Singularities, I
The Annals of Mathematics, 1976The author tackles the problem of defining equisingular infinitesimal deformations of normal singular points of algebraic surfaces \(S\). The technique is to study deformations of a resolution \(f: X\to S\) of the singularity \(x \in S\) which preserve the essential numerical (topological) data of the exceptional curve \(E=f^{-1}(x)\), and which blow ...
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