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J. Sib. Fed. Univ. Math. Phys., 2008, Volume 1, Issue 2, Pages 105–124 (Mi jsfu12)  

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

Multi-Logarithmic Differential Forms on Complete Intersections

Alexandr G. Aleksandrova, Avgust K. Tsikhb

a Institute of Control Sciences, Russian Academy of Sciences
b Institute of Mathematics, Siberian Federal University

Abstract: We construct a complex $\Omega_S^\bullet(\log C)$ of sheaves of multi-logarithmic differential forms on a complex analytic manifold $S$ with respect to a reduced complete intersection $C\subset S$, and define the residue map as a natural morphism from this complex onto the Barlet complex $\omega_C^\bullet$ of regular meromorphic differential forms on $C$. It follows then that sections of the Barlet complex can be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the residue map can be described explicitly in terms of certain integration current.

Keywords: complete intersection, multi-logarithmic differential forms, regular meromorphic differential forms, Poincaré residue, logarithmic residue, Grothendieck duality, residue current.

Full text: PDF file (398 kB)
References: PDF file   HTML file
UDC: 517.55
Received: 02.02.2008
Received in revised form: 10.04.2008
Accepted: 12.04.2008
Language:

Citation: Alexandr G. Aleksandrov, Avgust K. Tsikh, “Multi-Logarithmic Differential Forms on Complete Intersections”, J. Sib. Fed. Univ. Math. Phys., 1:2 (2008), 105–124

Citation in format AMSBIB
\Bibitem{AleTsi08}
\by Alexandr~G.~Aleksandrov, Avgust~K.~Tsikh
\paper Multi-Logarithmic Differential Forms on Complete Intersections
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2008
\vol 1
\issue 2
\pages 105--124
\mathnet{http://mi.mathnet.ru/jsfu12}
\elib{https://elibrary.ru/item.asp?id=11482590}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Bushueva, “On isotopies and homologies of subvarieties of toric varieties”, Siberian Math. J., 51:5 (2010), 776–788  mathnet  crossref  mathscinet  isi
    2. A. G. Aleksandrov, “The Multiple Residue and the Weight Filtration on the Logarithmic de Rham Complex”, Funct. Anal. Appl., 47:4 (2013), 247–260  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Schulze M., Tozzo L., “A Residual Duality Over Gorenstein Rings With Application to Logarithmic Differential Forms”, J. Singul., 18 (2018), 272–299  crossref  mathscinet  zmath  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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