Homology of complex projective hypersurfaces with isolated singularities

Miller, John L.

doi:10.1090/S0002-9939-1976-0418104-2

Homology of complex projective hypersurfaces with isolated singularities
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by John L. Miller PDF

Proc. Amer. Math. Soc. 56 (1976), 310-312 Request permission

Abstract:

We use information concerning the homology of links and Milnor fibers at each singularity of a hypersurface $\tilde V$, of degree $d$ in $C{P^{n + 1}}$ with only isolated singularities, to determine $\tilde V$’s homology except for the question of torsion in ${H_n}(\tilde V;Z)$.

References

Aldo Andreotti and Theodore Frankel, The second Lefschetz theorem on hyperplane sections, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 1–20. MR 0271106
F. Hirzebruch, W. D. Neumann, and S. S. Koh, Differentiable manifolds and quadratic forms, Lecture Notes in Pure and Applied Mathematics, Vol. 4, Marcel Dekker, Inc., New York, 1971. Appendix II by W. Scharlau. MR 0341499
Alan Howard, On the homotopy groups of an affine algebraic hypersurface, Ann. of Math. (2) 84 (1966), 197–216. MR 214095, DOI 10.2307/1970518
Mitsuyoshi Kato and Yukio Matsumoto, Simply connected surgery of submanifolds in codimension two. I, J. Math. Soc. Japan 24 (1972), 586–608. MR 307249, DOI 10.2969/jmsj/02440586
J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
John Milnor and Peter Orlik, Isolated singularities defined by weighted homogeneous polynomials, Topology 9 (1970), 385–393. MR 293680, DOI 10.1016/0040-9383(70)90061-3
Emery Thomas and John Wood, On manifolds representing homology classes in codimension $2$, Invent. Math. 25 (1974), 63–89. MR 383438, DOI 10.1007/BF01389998