Journal of Algebraic Geometry Journal of Algebraic Geometry

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Nodes and the Hodge conjecture

Author(s): R. P. Thomas
Journal: J. Algebraic Geom. 14 (2005), 177-185.
Posted: March 15, 2004
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Abstract | References | Additional information

Abstract: The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

References:

[AK]
A. Altman and S. Kleiman. Bertini theorems for hypersurface sections containing a subscheme. Commun. Algebra 7, 775-790 (1979).

[Cl]
H. Clemens. Double solids. Adv. in Math. 47, 107-230 (1983).

[GH]
P. Griffiths and J. Harris. Principles of algebraic geometry. Wiley, New York, 1978.

[Kl]
S. Kleiman. Geometry on Grassmannians and applications to splitting bundles and smoothing cycles. Publ. Math., Inst. Hautes Étud. Sci. 36, 281-297 (1969).

[Sch]
C. Schoen. Algebraic cycles on certain desingularized nodal hypersurfaces. Math. Ann. 270, 17-27 (1985).

Additional Information:

R. P. Thomas
Affiliation: Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2AZ United Kingdom
Email: rpwt@ic.ac.uk

PII: S 1056-3911(04)00378-9
Received by editor(s): May 22, 2003
Posted: March 15, 2004

Journal of Algebraic Geometry
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