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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 1–17 (Mi faa3178)  

This article is cited in 1 scientific paper (total in 1 paper)

The Index of Differential Forms on Complete Intersections

A. G. Aleksandrov

V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow

Abstract: The article is devoted to the development of a homological approach to the problem of calculating the local topological index of holomorphic differential $1$-forms given on complex space. In the study of complete intersections our method is based on the construction of Lebelt and Cousin resolutions, as well as on the simplest properties of the generalized and usual Koszul complexes, regular meromorphic differential forms, and the residue map. In particular, we show that the index of a differential $1$-form with an isolated singularity is equal to the dimension of the local analytical algebra of a zero-dimensional germ which is determined by the ideal generated by the interior product of the form and all Hamiltonian vector fields of the complete intersection. Moreover, in the quasihomogeneous case, the index can be expressed explicitly in terms of values of classical symmetric functions. We also discuss some other methods for computing the homological index of $1$-forms given on analytic spaces with singularities of various types.

Keywords: index of differential forms, homological index, isolated complete intersection singularities, de Rham complex, Koszul complex, regular meromorphic forms

DOI: https://doi.org/10.4213/faa3178

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English version:
Functional Analysis and Its Applications, 2015, 49:1, 1–14

Bibliographic databases:

UDC: 515.17
Received: 15.02.2013

Citation: A. G. Aleksandrov, “The Index of Differential Forms on Complete Intersections”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 1–17; Funct. Anal. Appl., 49:1 (2015), 1–14

Citation in format AMSBIB
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\by A.~G.~Aleksandrov
\paper The Index of Differential Forms on Complete Intersections
\jour Funktsional. Anal. i Prilozhen.
\yr 2015
\vol 49
\issue 1
\pages 1--17
\mathnet{http://mi.mathnet.ru/faa3178}
\crossref{https://doi.org/10.4213/faa3178}
\zmath{https://zbmath.org/?q=an:06485781}
\elib{http://elibrary.ru/item.asp?id=23421400}
\transl
\jour Funct. Anal. Appl.
\yr 2015
\vol 49
\issue 1
\pages 1--14
\crossref{https://doi.org/10.1007/s10688-015-0078-z}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924942546}


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  • https://doi.org/10.4213/faa3178
  • http://mi.mathnet.ru/eng/faa/v49/i1/p1

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Aleksandrov, “Differential Forms on Quasihomogeneous Noncomplete Intersections”, Funct. Anal. Appl., 50:1 (2016), 1–16  mathnet  crossref  crossref  mathscinet  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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