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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
MathSciNet review:
2092131
Retrieve article in:
PDF
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
DOI:
10.1090/S1056-3911-04-00378-9
PII:
S 1056-3911(04)00378-9
Received by editor(s):
May 22, 2003
Posted:
March 15, 2004
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