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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Generic sections of essentially isolated determinantal singularities

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Author(s):
Brasselet, Jean-Paul [1] ; Chachapoyas, Nancy [2] ; Ruas, Maria A. S. [3]
Total Authors: 3
Affiliation:
[1] Univ Aix Marseille, UMR 7373, Inst Math Marseille, Campus Luminy Case 907, F-13288 Marseille 9 - France
[2] Univ Fed Itajuba, Inst Matemat & Comp, Ave BPS, 1303 Pinheirinho, BR-37500903 Itajuba, MG - Brazil
[3] ICMC USP, Inst Ciencias Matemat & Comp, Av Trabalhador Sao Carlense, 400 Ctr, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF MATHEMATICS; v. 28, n. 11 OCT 2017.
Web of Science Citations: 3
Abstract

We study the essentially isolated determinantal singularities (EIDS), defined by Ebeling and Gusein-Zade {[}S. M. Gusein-Zade and W. Ebeling, On the indices of 1-forms on determinantal singularities, Tr. Mat. Inst. Steklova 267 (2009) 119-131], as a generalization of isolated singularity. We prove in dimension 3, a minimality theorem for the Milnor number of a generic hyperplane section of an EIDS, generalizing the previous results by Snoussi in dimension 2. We define strongly generic hyperplane sections of an EIDS and show that they are still EIDS. Using strongly general hyperplanes, we extend a result of Le concerning the constancy of the Milnor number. (AU)

FAPESP's process: 15/06697-9 - Characteristic classes and intersection homology
Grantee:João Carlos Ferreira Costa
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 10/09736-1 - Milnor classes and polar varieties
Grantee:Nancy Carolina Chachapoyas Siesquén
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 14/00304-2 - Singularities of differentiable mappings: theory and applications
Grantee:Maria Aparecida Soares Ruas
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 11/20082-6 - Milnor classes and polar varieties
Grantee:Nancy Carolina Chachapoyas Siesquén
Support Opportunities: Scholarships abroad - Research Internship - Doctorate