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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 4, Pages 3–22
DOI: https://doi.org/10.4213/faa3573 (Mi faa3573) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Differential Forms on Zero-Dimensional Singularities

A. G. Aleksandrov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
Full-text PDF (293 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa3573
Abstract: In this paper we discuss some problems of the deformation theory of zero-dimensional singularities, which are closely related to the study of properties of differential forms and the Poincaré–de Rham complex. We also investigate the cotangent homology and cohomology of zerodimensional singularities, compute the basic analytic invariants for certain types of such singularities, and examine in detail some interesting examples and applications.
Keywords: multiple points, fat points, thick points, differential forms, Poincaré lemma, cotangent homology, complete intersections, determinantal singularities, vector fields.
Received: 28.02.2018
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 4, Pages 241–257
DOI: https://doi.org/10.1007/s10688-018-0235-2
Bibliographic databases:
Document Type: Article
UDC: 515.17
Language: Russian
Citation: A. G. Aleksandrov, “Differential Forms on Zero-Dimensional Singularities”, Funktsional. Anal. i Prilozhen., 52:4 (2018), 3–22; Funct. Anal. Appl., 52:4 (2018), 241–257
Citation in format AMSBIB
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\paper Differential Forms on Zero-Dimensional Singularities
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\pages 3--22
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\jour Funct. Anal. Appl.
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\pages 241--257
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  • https://www.mathnet.ru/eng/faa3573
  • https://doi.org/10.4213/faa3573
  • https://www.mathnet.ru/eng/faa/v52/i4/p3
    • This publication is cited in the following 3 articles:
    1. A. G. Aleksandrov, “On a sharp lower bound for the Tjurina number of zero-dimensional complete intersections”, Funct. Anal. Appl., 57:1 (2023), 1–17  mathnet  crossref  crossref
    2. A. G. Aleksandrov, “On Milnor and Tyurina numbers of zero-dimensional singularities”, Funct. Anal. Appl., 56:1 (2022), 1–18  mathnet  crossref  crossref
    3. A. G. Aleksandrov, “Deformations of commutative Artinian algebras”, St. Petersburg Math. J., 34:6 (2023), 889–911  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Abstract page:412
    Full-text PDF :80
    References:54
    First page:18
     
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