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The Hodge conjecture for fourfolds admitting a covering by rational curves. (English) Zbl 0373.14006


MSC:

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14M20 Rational and unirational varieties
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References:

[1] Beauville, A.: Variétés de Prym et jacobiennes intermediaires. Thèse, Paris 1977 · Zbl 0368.14018
[2] Bloch, S.: An example in the theory of algebraic cycles, in Algebraic K-theory, Evanston 1976. Lecture Notes in Mathematics 551. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0358.14003
[3] Bloch, S., Murre, J.P.: On the Chow groups of-certain types of Fano threefolds (to appear) · Zbl 0426.14018
[4] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Annals of Math.79, 109-326 (1964) · Zbl 0122.38603 · doi:10.2307/1970486
[5] Kleiman, S.L.: Algebraic cycles and the Weil conjectures, in Dix exposés sur la cohomologie des schémas. Amsterdam: North-Holland 1968
[6] Murre, J.P.: On the Hodge conjecture for unirational fourfolds. Indag. Math.80, 230-232 (1977) · Zbl 0352.14006
[7] Predonzan, A.: Intorno agliS k giacenti sulla varietà intersezione completa di più forme. Rend. Acc. Lincei5, 238-242 (1948) · Zbl 0036.37704
[8] Tennison, B.R.: On the quartic threefold. Proc. London Math. Soc.29, 714-734 (1974) · Zbl 0308.14005 · doi:10.1112/plms/s3-29.4.714
[9] Zucker, S.: The Hodge conjecture for cubic fourfolds. Compositio Math.34, 199-210 (1977) · Zbl 0347.14005
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