Nodes and the Hodge conjecture
Author:
R. P. Thomas
Journal:
J. Algebraic Geom. 14 (2005), 177-185
DOI:
https://doi.org/10.1090/S1056-3911-04-00378-9
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.
[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).
[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
Email:
rpwt@ic.ac.uk
Received by editor(s):
May 22, 2003
Published electronically:
March 15, 2004
