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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 1, Pages 1–19 (Mi faa3223)  

This article is cited in 3 scientific papers (total in 3 papers)

Differential Forms on Quasihomogeneous Noncomplete Intersections

A. G. Aleksandrov

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

Abstract: In this article, we discuss a few simple methods for computing the Poincaré series of modules of differential forms given on quasihomogeneous noncomplete intersections of various types. Among them are curves associated with a semigroup, bouquets of such curves, affine cones over rational or elliptic curves, and normal determinantal and toric varieties, including some types of quotient singularities, as well as cones over the Veronese embedding of projective spaces or over the Segre embedding of products of projective spaces, rigid singularities, fans, etc. In many cases, correct formulas can be derived without resorting to analysis of complicated resolvents or using computer systems of algebraic calculations. The obtained results allow us to compute the basic invariants of singularities in an explicit form by means of elementary operations on rational functions.

Keywords: differential forms, Poincaré complex, de Rham complex, graded singularities, determinantal singularities, rigid singularities, fans.

DOI: https://doi.org/10.4213/faa3223

Full text: PDF file (259 kB)
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English version:
Functional Analysis and Its Applications, 2016, 50:1, 1–16

Bibliographic databases:

UDC: 515.17
Received: 04.03.2015

Citation: A. G. Aleksandrov, “Differential Forms on Quasihomogeneous Noncomplete Intersections”, Funktsional. Anal. i Prilozhen., 50:1 (2016), 1–19; Funct. Anal. Appl., 50:1 (2016), 1–16

Citation in format AMSBIB
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\by A.~G.~Aleksandrov
\paper Differential Forms on Quasihomogeneous Noncomplete Intersections
\jour Funktsional. Anal. i Prilozhen.
\yr 2016
\vol 50
\issue 1
\pages 1--19
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\jour Funct. Anal. Appl.
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  • https://doi.org/10.4213/faa3223
  • http://mi.mathnet.ru/eng/faa/v50/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, “Logarithmic differential forms on varieties with singularities”, Funct. Anal. Appl., 51:4 (2017), 245–254  mathnet  crossref  crossref  isi  elib
    2. A. G. Aleksandrov, “Differential Forms on Zero-Dimensional Singularities”, Funct. Anal. Appl., 52:4 (2018), 241–257  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Aleksandrov A.G., “Analytic Invariants of Multiple Points”, Methods Appl. Anal., 25:3 (2018), 167–203  mathscinet  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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