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Decompositions of hypersurface singularities oftype J k , 0

Piotr Jaworski (1994)

Annales Polonici Mathematici

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.

Déformations équivariantes des courbes semistables

José Bertin, Sylvain Maugeais (2005)

Annales de l’institut Fourier

Nous étudions la théorie des déformations des revêtements galoisiens sauvagement ramifiés entre courbes stables. On examine d’abord les problèmes locaux, point double formel avec pour groupe d’inertie un p -groupe, puis le cas global. On compare enfin les obstructions globales au relèvement aux obstructions locales.

Deformations of free and linear free divisors

Michele Torielli (2013)

Annales de l’institut Fourier

We study deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates the deformation spaces. This cohomology turns out to be zero for all reductive linear free divisors and to be constructible for Koszul free divisors and weighted homogeneous free divisors.

Deforming syzygies of liftable modules and generalised Knörrer functors

Runar Ile (2007)

Collectanea Mathematica

Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.

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