Brieskorn and the monodromy
| Autor: | Jean-Paul Brasselet, Marcos Sebastiani |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
PERIODS 010308 nuclear & particles physics Applied Mathematics media_common.quotation_subject Complete intersection ALGEBRAIC-MANIFOLDS 01 natural sciences Hypersurface Monodromy Originality INTEGRALS 0103 physical sciences Gravitational singularity Geometry and Topology [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Connection (algebraic framework) media_common Mathematics |
| Zdroj: | Journal of Singularities Journal of Singularities, 2018, 18, pp.84-104. ⟨10.5427/jsing.2018.18f⟩ Journal of Singularities, Worldwide Center of Mathematics, LLC, 2018, 18, pp.84-104. ⟨10.5427/jsing.2018.18f⟩ |
| ISSN: | 1949-2006 |
| DOI: | 10.5427/jsing.2018.18f⟩ |
| Popis: | International audience; Brieskorn’s paper “Die Monodromie der isolierten Singularit ̈aten von Hyperfl ̈aschen,” pub- lished in 1970 in Manuscripta Mathematica, gave a new insight to the theory of monodromy and Gauß-Manin connections. The paper, written in the framework of isolated hypersurface singularities, has been generalized for isolated complete intersection singularities by G.-M. Greuel in 1975 [10]. In the following times and also more recently, a long list of authors, among them P. Deligne [7], W. Ebeling [8], H. Hamm [12], Lˆe D. T. [20], B. Malgrange [24], D.Siersma [37] etc. provided generalizations and developments of the monodromy theory. The regularity of the Gauß-Manin connection, proved by Brieskorn in the framework of isolated hypersurface singularities has been proved and developed in various situations by many authors, among them G.-M. Greuel [10], C. Hertling [15], F. Pham [28], K. Saito [29], M. Saito [30], J. Scherk and J.H.M. Steenbrink [31], M. Schulze [32], A. Varchenko [38], etc.There are many surveys concerning the various aspects of monodromy and including developments of the theory. In particular, Ebeling’s survey [8] shows very well the importance of Brieskorn’s article as well as developments and generalisations of the Brieskorn’s results. Siersma’s survey [37] deals with the non-isolated case, and presents new results in this framework.The present paper, based on ideas of the second author [34, 35, 36], does not pretend any originality. It is not devoted to specialists, but to “beginners”. The aim of the paper is to introduce monodromy theory and provide some elementary view about the Brieskorn paper. Our aim is not to replace the reading of this very important Brieskorn article, but hopefully to encourage one to read it. |
| Databáze: | OpenAIRE |
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