×

zbMATH — the first resource for mathematics

Algebraic cycles and Hodge theory on generalized Reye congruences. (English) Zbl 0816.14004
The paper is devoted to the study of the general \(n\)-dimensional complete intersections of symmetric divisors of bidegree (1,1) in \(\mathbb{P}^{n+1} \times \mathbb{P}^{n+1}\). These varieties are generalizations of the classical Reye congruence. In particular the generalized Grothendieck Hodge conjecture is checked for these varieties.
Reviewer: A.Buium (Bonn)

MSC:
14C25 Algebraic cycles
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14M10 Complete intersections
14N05 Projective techniques in algebraic geometry
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] F. Bardelli , On Grothendieck’s generalized Hodge conjecture for a family of threefold with trivial canonical bundle . J. reine und angew. Math. 422 (1991), 165-200. · Zbl 0728.14007 · doi:10.1515/crll.1991.422.165 · crelle:GDZPPN002209101 · eudml:153378
[2] A. Beauville , Complex algebraic surfaces . London Math. Soc. Lcture Note Series 68. · Zbl 0512.14020
[3] P. Deligne , Theorie de Hodge III . Publ. Math. I.H.E.S. 44 (1974), 5-78. · Zbl 0237.14003 · doi:10.1007/BF02685881 · numdam:PMIHES_1974__44__5_0 · eudml:103935
[4] P.A. Griffiths , Periods of integrals on algebraic manifolds, II . Am. Jour. of Math. 90 (1968), 805-864. · Zbl 0183.25501 · doi:10.2307/2373485
[5] A. Grothendieck , Hodge’s general conjecture is false for trivial reasons . Topology 8 (1969), 299-303. · Zbl 0177.49002 · doi:10.1016/0040-9383(69)90016-0
[6] K. Kodaira , A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds . Ann. of Math. 75 (1962), 146-162. · Zbl 0112.38404 · doi:10.2307/1970424
[7] K. Lamotke , The topology of complex projective varieties after S. Lefschetz . Topology 20 (1981), 15-51. · Zbl 0445.14010 · doi:10.1016/0040-9383(81)90013-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.