Geodesic
A Griffiths' Theorem for Varieties with Isolated Singularities
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 159-172.

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By the fundamental work of Griffiths one knows that, under suitable assumption, homological and algebraic equivalence do not coincide for a general hypersurface section of a smooth projective variety Y. In the present paper we prove the same result in case Y has isolated singularities. 
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di Gennaro, Vincenzo; Franco, Davide; Marini, Giambattista. A Griffiths' Theorem for Varieties with Isolated Singularities. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 159-172. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_1_a8/

[DGF] V. Di Gennaro - D. Franco, Monodromy of a family of hypersurfaces, Ann. Scient. Éc. Norm. Sup., 42 (2009), 517-529. | fulltext EuDML | DOI | MR | Zbl

[D1] A. Dimca, Singularity and Topology of Hypersurfaces, Universitext, Springer, 1992. | DOI | MR

[D2] A. Dimca, Sheaves in Topology, Universitext, Springer, 2004. | DOI | MR

[FOV] H. Flenner - L. O'Carroll - W. Vogel, Joins and Intersections, Monographs in Mathematics, Springer, 1999. | DOI | MR

[F1] W. Fulton, Intersection Theory, Ergebnisse Math. Grenzg., 2 (Springer, 1984). | DOI | MR | Zbl

[F2] W. Fulton, Young Tableaux With Applications to Representation Theory and Geometry, London Mathematical Society Student Texts 35, Cambridge University Press, 1977. | MR | Zbl

[Gre] M. Green, Griffiths' infinitesimal invariant and the Abel-Jacobi map, J. Differ. Geom., 29 (1989), 545-555. | MR | Zbl

[Gri] P. Griffiths, On the periods of certain rational integrals, I, II, Ann. of Math., 90 (1969), 460-541. | DOI | MR | Zbl

[H] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math., 52 (Springer, 1977). | MR

[L] R. Lazarsfeld, Positivity in Algebraic Geometry I. Classical Setting: Line Bundles and Linear Series, Springer, 2004. | DOI | MR | Zbl

[N] M. Nori, Algebraic cycles and Hodge theoretic connectivity, Invent. Math., 111 (1993), 349-373. | fulltext EuDML | DOI | MR | Zbl

[Sh] T. Shioda, Algebraic cycles on a certain hypersurface, in Algebraic Geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., 1016 (Springer, 1983), 271-294. | DOI | MR

[Sp] E. H. Spanier, Algebraic Topology, Mc Graw-Hill Series in Higher Mathematics (1966). | MR

[V1] C. Voisin, Hodge Theory and Complex Algebraic Geometry I, Cambridge Studies in Advanced Mathematics 76, Cambridge University Press (2002). | DOI | MR | Zbl

[V2] C. Voisin, Hodge Theory and Complex Algebraic Geometry II, Cambridge Studies in Advanced Mathematics 77, Cambridge University Press (2003). | DOI | MR | Zbl