A Griffiths' Theorem for Varieties with Isolated Singularities

Vincenzo di Gennaro; Davide Franco; Giambattista Marini

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 1, page 159-172
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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di Gennaro, Vincenzo, Franco, Davide, and Marini, Giambattista. "A Griffiths' Theorem for Varieties with Isolated Singularities." Bollettino dell'Unione Matematica Italiana 5.1 (2012): 159-172. <http://eudml.org/doc/290950>.

@article{diGennaro2012,
abstract = {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.},
author = {di Gennaro, Vincenzo, Franco, Davide, Marini, Giambattista},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {159-172},
publisher = {Unione Matematica Italiana},
title = {A Griffiths' Theorem for Varieties with Isolated Singularities},
url = {http://eudml.org/doc/290950},
volume = {5},
year = {2012},
}

TY - JOUR
AU - di Gennaro, Vincenzo
AU - Franco, Davide
AU - Marini, Giambattista
TI - A Griffiths' Theorem for Varieties with Isolated Singularities
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/2//
PB - Unione Matematica Italiana
VL - 5
IS - 1
SP - 159
EP - 172
AB - 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.
LA - eng
UR - http://eudml.org/doc/290950
ER -

References

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  11. NORI, M., Algebraic cycles and Hodge theoretic connectivity, Invent. Math., 111 (1993), 349-373. Zbl0822.14008MR1198814DOI10.1007/BF01231292
  12. SHIODA, T., Algebraic cycles on a certain hypersurface, in Algebraic Geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., 1016 (Springer, 1983), 271-294. MR726430DOI10.1007/BFb0099967
  13. SPANIER, E. H., Algebraic Topology, Mc Graw-Hill Series in Higher Mathematics (1966). MR210112
  14. VOISIN, C., Hodge Theory and Complex Algebraic Geometry I, Cambridge Studies in Advanced Mathematics76, Cambridge University Press (2002). Zbl1005.14002MR1967689DOI10.1017/CBO9780511615344
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