Abstract
A nonsingular hypersurface X in \(\mathbb{C}P^{n-1}\) with n≥3 is studied. The main result of the paper says that the homology coming from the affine part of a hypersurface of smaller degree forms a direct summand in the homology of X, which is independent over integers with the class of a multiple hyperplane section. The proof is outlined. Bibliography: 3 titles.
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REFERENCES
A. Dimca, Singularities and Topology of Hypersurfaces, Springer-Verlag, New York-Berlin (1992).
O. A. Ivanov and N. Yu. Netsvetaev, “On the intersection form of the result of pasting together manifolds with nondegenerate intersection forms” Zap. Nauchn. Semin. POMI, 231, 169-179 (1995).
N. Yu. Netsvetaev, “On the topological structure of complex hypersurfaces with quadratic singularities” Zap. Nauchn. Semin. POMI, 231, 210-221 (1995).
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Netsvetaev, N.Y. Homology of a Perturbation of a Complex Projective Hypersurface. Journal of Mathematical Sciences 110, 2872–2874 (2002). https://doi.org/10.1023/A:1015318816402
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DOI: https://doi.org/10.1023/A:1015318816402