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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Nodes and the Hodge conjecture

Author: R. P. Thomas
Journal: J. Algebraic Geom. 14 (2005), 177-185
Published electronically: March 15, 2004
MathSciNet review: 2092131
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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 [Enhancements On Off] (What's this?)

    [AK]AK A. Altman and S. Kleiman. Bertini theorems for hypersurface sections containing a subscheme. Commun. Algebra 7, 775–790 (1979). [Cl]Cl H. Clemens. Double solids. Adv. in Math. 47, 107–230 (1983). [GH]GH P. Griffiths and J. Harris. Principles of algebraic geometry. Wiley, New York, 1978. [Kl]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]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
MR Author ID: 636321

Received by editor(s): May 22, 2003
Published electronically: March 15, 2004