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Limit trees and generic discriminants of minimal surface singularities

Eric Akéké (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

According to R. Bondil the dual graph of the minimal resolution of a minimal normal surface singularity determines the generic discriminant of that singularity. In this article we give with combinatorial arguments the link between the limit trees and the generic discriminants of minimal normal surface singularities. The weighted limit trees of a minimal surface singularity determine the generic discriminant of that singularity.

Local embeddings of lines in singular hypersurfaces

Guangfeng Jiang, Dirk Siersma (1999)

Annales de l'institut Fourier

Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.

Loop groups, elliptic singularities and principal bundles over elliptic curves

Stefan Helmke, Peter Slodowy (2003)

Banach Center Publications

There is a well known relation between simple algebraic groups and simple singularities, cf. [5], [28]. The simple singularities appear as the generic singularity in codimension two of the unipotent variety of simple algebraic groups. Furthermore, the semi-universal deformation and the simultaneous resolution of the singularity can be constructed in terms of the algebraic group. The aim of these notes is to extend this kind of relation to loop groups and simple elliptic singularities. It is the...

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