Real and complex integral closure, Lipschitz equisingularity and applications on square matrices

Thiago Filipe da Silva, Nivaldo de Góes Grulha Júnior, and Miriam da Silva Pereira

Journal of Singularities
volume 22 (2020), 215-226

Received: 10 April 2019. Received in revised form: 4 February 2020.

DOI: 10.5427/jsing.2020.22o

Add a reference to this article to your citeulike library.

Abstract:

Recently the authors investigated the Lipschitz triviality of simple germs of matrices. In this work, we improve some previous results and we present an extension of an integral closure result for the real setting. These tools are applied to investigate classes of square matrices singularities classified by Bruce and Tari.

2010 Mathematical Subject Classification:

32S15, 14J17, 32S60

Key words and phrases:

Bi-Lipschitz Equisingularity, Real and Complex integral closure, The double structure, Finite Determinacy, Canonical vector fields

Author(s) information:

Thiago Filipe da Silva
Departamento de Matemática
Universidade Federal do Espírito Santo
Av. Fernando Ferrari, 514 - Goiabeiras
29075-910 - Vitória - ES, Brazil
email: thiago.silva@ufes.br

Nivaldo de Góes Grulha Júnior
Instituto de Ciências Matemáticas e de Computaćão - USP
Av. Trabalhador São Carlense, 400 - Centro
13566-590 - São Carlos - SP, Brazil
email: njunior@icmc.usp.br

Miriam da Silva Pereira
Departamento de Matemática
Universidade Federal da Paraíba
58.051-900 João Pessoa, Brazil
email: miriam@mat.ufpb.br