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Mat. Sb. (N.S.), 1975, Volume 97(139), Number 2(6), Pages 301–315 (Mi msb3653)  

On the homological structure of a fibering of an algebraic variety with isolated sungularities

A. B. Zhizhchenko


Abstract: We study a fibering of a complex projective variety $W$ with isolated singularities of Pham type in the fibers. We investigate the connection between the homology groups $H_*(W)$ and the homology groups $H_*(F_0)$ of a general fiber $F_0$ and local data. We shall explain how the relation between the structure of the homology groups $H_{n+2}(W),…,H_{2n}(W)$, where $n=\dim_{\mathbf C}W$, and the homology groups of a nonsingular fiber is trivial, while the mean groups $H_{n+1}(W)$, $H_n(W)$ and $H_{n-1}(W)$ can be expressed in terms of the homology groups of the general fiber $F_0$ together with the kernels and cokernels of the morphisms $r_*^i\colon H_*(F_0)\to H_*(F_i)$, where $F_1,…,F_s$ are the singular fibers of the fibering, and the $r_*^i$ correspond to the mappings (retractions) of the nonsingular fiber onto the singular ones.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1975, 26:2, 280–293

Bibliographic databases:

UDC: 513.836
MSC: Primary 14B05; Secondary 14D05, 14E15
Received: 20.02.1975

Citation: A. B. Zhizhchenko, “On the homological structure of a fibering of an algebraic variety with isolated sungularities”, Mat. Sb. (N.S.), 97(139):2(6) (1975), 301–315; Math. USSR-Sb., 26:2 (1975), 280–293

Citation in format AMSBIB
\Bibitem{Zhi75}
\by A.~B.~Zhizhchenko
\paper On~the homological structure of a~fibering of an algebraic variety with isolated sungularities
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 97(139)
\issue 2(6)
\pages 301--315
\mathnet{http://mi.mathnet.ru/msb3653}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=407015}
\zmath{https://zbmath.org/?q=an:0332.14005}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 26
\issue 2
\pages 280--293
\crossref{https://doi.org/10.1070/SM1975v026n02ABEH002481}


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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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