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Determinacy of determinantal varieties

  • Imran Ahmed
  • Maria Aparecida Soares Ruas
Article

Abstract

A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of an \(m\times n\)-matrix. In this note, we consider \(\mathcal {G}\)-finite determinacy of matrices defining a special class of determinantal varieties. They are called essentially isolated determinantal singularities (EIDS) and were defined by Ebeling and Gusein-Zade (Singul Appl 267:119–131, 2009). In this note, we prove that matrices parametrized by generic homogeneous forms of degree d define EIDS. It follows that \(\mathcal {G}\)-finite determinacy of matrices holds in general. As a consequence, EIDS of a given type (mnt) holds in general.

Mathematics Subject Classification

Primary 32S05 58K40 Secondary 14B05 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyLahorePakistan
  2. 2.Departamento de Matemática, Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil

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