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EFFECTIVE REGULARITY CRITERIA FOR ANALYTIC MAPPINGS

EFFECTIVE REGULARITY CRITERIA FOR ANALYTIC MAPPINGS DEMONSTRATIO MATHEMATICAVol. XLIIINo 22010Janusz AdamusEFFECTIVE REGULARITY CRITERIA FORANALYTIC M A P P I N G SAbstract. We survey recent developments in the study of singularities of complexanalytic mappings from a local algebraic viewpoint. We present several effective criteria forvarious modes of regularity of complex-analytic mappings in terms of vertical componentsin fibred powers of the mappings.Contents1. Introduction2. Analytic tensor product and fibred product3. Openness vs.flatness4. Vertical components and variation of fibre dimension5. Vertical components and Gabrielov regularity6. Homological algebra apparatus7. Vertical components andflatness8. Algebraic caseReferences2352422442462492522542592611. IntroductionThe purpose of this paper is to provide a systematic exposition of acertain new method of analysis of the local geometry of complex-analyticmappings. We study the relationship between degeneracies in the familyof fibres of an analytic mapping and the existence of the so-called verticalcomponents in fibred powers of the mapping. There are, in fact, two natural notions of a vertical component (algebraic and geometric) and we areinterested also in the relationship between them.2000 Mathematics Subject Classification: Primary 13H05, 32B99; Secondary 13P99.Key words and phrases: flat, open, Gabrielov regular, torsion-free, fibred power, vertical component, analytic tensor product, complex analytic geometry.Research partially supported by the Natural Sciences and Engineering Research Council of Canada.236J. AdamusWe gathered here a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

EFFECTIVE REGULARITY CRITERIA FOR ANALYTIC MAPPINGS

Adamus, Janusz
Demonstratio Mathematica , Volume 43 (2): 28 – Apr 1, 2010
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References (22)

Publisher
de Gruyter
Copyright
© by Janusz Adamus
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2010-0203
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLIIINo 22010Janusz AdamusEFFECTIVE REGULARITY CRITERIA FORANALYTIC M A P P I N G SAbstract. We survey recent developments in the study of singularities of complexanalytic mappings from a local algebraic viewpoint. We present several effective criteria forvarious modes of regularity of complex-analytic mappings in terms of vertical componentsin fibred powers of the mappings.Contents1. Introduction2. Analytic tensor product and fibred product3. Openness vs.flatness4. Vertical components and variation of fibre dimension5. Vertical components and Gabrielov regularity6. Homological algebra apparatus7. Vertical components andflatness8. Algebraic caseReferences2352422442462492522542592611. IntroductionThe purpose of this paper is to provide a systematic exposition of acertain new method of analysis of the local geometry of complex-analyticmappings. We study the relationship between degeneracies in the familyof fibres of an analytic mapping and the existence of the so-called verticalcomponents in fibred powers of the mapping. There are, in fact, two natural notions of a vertical component (algebraic and geometric) and we areinterested also in the relationship between them.2000 Mathematics Subject Classification: Primary 13H05, 32B99; Secondary 13P99.Key words and phrases: flat, open, Gabrielov regular, torsion-free, fibred power, vertical component, analytic tensor product, complex analytic geometry.Research partially supported by the Natural Sciences and Engineering Research Council of Canada.236J. AdamusWe gathered here a

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Demonstratio Mathematica – de Gruyter

Published: Apr 1, 2010

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