A'Campo's theorem on the discriminant
type: Item
instance of: scholarly article
title: A'Campo's theorem on the discriminant
zbMATH Open document ID: 0839.58013
DOI: 10.1007/BF01076494
author: G. G. Il'yuta
publication date: 1995-09-27T00:00:00Z
review text: The Dynkin diagrams of singularities can be trees only for simple critical points. This result by N. A'Campo, has not been advanced whatsoever in the direction of increase of modality, sharing the fate of many beautiful theorems on simple \(A - D - E\) singularities. Counterexamples to naive conjectures were constructed by W. Ebeling. In the present paper we also remain in the modality 0. A'Campo's theorem and a theorem close to it stating that only the standard Dynkin diagrams of simple singularities contain no edges of negative weight are generalized to degenerate decompositions of a singularity that appear in the base of its bounded miniversal deformation. We also prove A'Campo's theorem for boundary singularities and a block version of the formula representing the Coxeter operator as a product of upper and lower triangular matrices (in the terminology of the theory of singularities, this is a formula relating the variation and the classical monodromy operators). Moreover, for real deformations of singularities, we prove a formula relating the classical monodromy operator to the intersection form; some conjectures on monodromy of singularities are also stated.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 795612
zbMATH Keywords: A'Campo theorem
zbMATH Keywords: Dynkin diagrams
zbMATH Keywords: singularities
zbMATH Keywords: monodromy
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 795612