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.
@article{BUMI_2012_9_5_1_159_0, author = {Vincenzo di Gennaro and Davide Franco and Giambattista Marini}, title = {A Griffiths' Theorem for Varieties with Isolated Singularities}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {5}, year = {2012}, pages = {159-172}, zbl = {1256.14009}, mrnumber = {2919654}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_1_159_0} }
di Gennaro, Vincenzo; Franco, Davide; Marini, Giambattista. A Griffiths' Theorem for Varieties with Isolated Singularities. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 159-172. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_1_159_0/
[DGF] Monodromy of a family of hypersurfaces, Ann. Scient. Éc. Norm. Sup., 42 (2009), 517-529. | MR 2543331 | Zbl 1194.14016
- ,[D1] | MR 1194180
, Singularity and Topology of Hypersurfaces, Universitext, Springer, 1992.[D2] | MR 2050072
, Sheaves in Topology, Universitext, Springer, 2004.[FOV] | MR 1724388
- - , Joins and Intersections, Monographs in Mathematics, Springer, 1999.[F1] 2 (Springer, 1984). | MR 732620 | Zbl 0541.14005
, Intersection Theory, Ergebnisse Math. Grenzg.,[F2] 35, Cambridge University Press, 1977. | MR 1464693 | Zbl 0878.14034
, Young Tableaux With Applications to Representation Theory and Geometry, London Mathematical Society Student Texts[Gre] Griffiths' infinitesimal invariant and the Abel-Jacobi map, J. Differ. Geom., 29 (1989), 545-555. | MR 992330 | Zbl 0692.14003
,[Gri] On the periods of certain rational integrals, I, II, Ann. of Math., 90 (1969), 460-541. | MR 260733 | Zbl 0215.08103
,[H] 52 (Springer, 1977). | MR 463157
, Algebraic Geometry, Graduate Texts in Math.,[L] | MR 2095471 | Zbl 1093.14501
, Positivity in Algebraic Geometry I. Classical Setting: Line Bundles and Linear Series, Springer, 2004.[N] Algebraic cycles and Hodge theoretic connectivity, Invent. Math., 111 (1993), 349-373. | MR 1198814 | Zbl 0822.14008
,[Sh] Algebraic cycles on a certain hypersurface, in Algebraic Geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., 1016 (Springer, 1983), 271-294. | MR 726430
,[Sp] Algebraic Topology, Mc Graw-Hill Series in Higher Mathematics (1966). | MR 210112
,[V1] 76, Cambridge University Press (2002). | MR 1967689 | Zbl 1005.14002
, Hodge Theory and Complex Algebraic Geometry I, Cambridge Studies in Advanced Mathematics[V2] 77, Cambridge University Press (2003). | MR 1997577 | Zbl 1032.14002
, Hodge Theory and Complex Algebraic Geometry II, Cambridge Studies in Advanced Mathematics