Algebraic equivalence modulo rational equivalence on a cubic threefold

J. P. Murre

Compositio Mathematica (1972)

  • Volume: 25, Issue: 2, page 161-206
  • ISSN: 0010-437X

How to cite


Murre, J. P.. "Algebraic equivalence modulo rational equivalence on a cubic threefold." Compositio Mathematica 25.2 (1972): 161-206. <>.

author = {Murre, J. P.},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {161-206},
publisher = {Wolters-Noordhoff Publishing},
title = {Algebraic equivalence modulo rational equivalence on a cubic threefold},
url = {},
volume = {25},
year = {1972},

AU - Murre, J. P.
TI - Algebraic equivalence modulo rational equivalence on a cubic threefold
JO - Compositio Mathematica
PY - 1972
PB - Wolters-Noordhoff Publishing
VL - 25
IS - 2
SP - 161
EP - 206
LA - eng
UR -
ER -


  1. E. Bombieri And H.P.F. Swinnerton-Dyer [1] On the local zeta function of a cubic threefold. Annali Scuola Norm. Sup. di Pisa21 (1967), 1-29. Zbl0153.50501MR212019
  2. W.L. Chow [2] On equivalence classes of cycles in an algebraic variety. Annals of Math.64 (1956), 450-479. Zbl0073.37304MR82173
  3. C.H. Clemens And P.A. Griffiths [3] The intermediate Jacobian of the cubic three fold. Annals of Math.95 (1972), 281-356. Zbl0214.48302MR302652
  4. A. Grothendieck [4] Sur quelques propriétés fondamentales en théorie des intersections. Exposé 4; Séminaire C. Chevalley: Anneaux de Chow (1958), p. 4.01-4.36. 
  5. D. Mumford [5] Prym varieties. To be published. [6] The intermediate Jacobian of the cubic threefold. Private paper. 
  6. J.P. Murre [7] Intersection multiplicities of maximal connected bunches. Amer. J. of Math.80 (1958), 311-330. Zbl0083.36801MR93523
  7. L. Roth AND J.G. Semple [8] Introduction to algebraic geometry. Oxford. Clarendon Press, 1949. Zbl0041.27903MR34048
  8. P. Samuel [9] Relations d'équivalence en géométrie algébrique. Proc. Internat. Congress Math. Edinburgh1958, 470-487. Zbl0119.36901MR116010
  9. A. Weil [10] Foundations of Algebraic Geometry. Amer. Math. Soc. Coll. Publ. 29, 2nd Ed. 1962. Zbl0168.18701MR144898
  10. O. Zariski [11] Introduction to the problem of minimal models in the theory of algebraic surfaces. Publ. of the Math. Soc. Japan4, 1958. Zbl0093.33904MR97403
  11. A.M. Šermenev [12] On the motif of a cubic hypersurface. Izvestija Akad. Nauk S.S.S.R.34 (1970), 515-522 (Russian). Translation: Math. of U.S.S.R.4 (1970), 520-526. Zbl0234.14013MR262245

Citations in EuDML Documents

  1. J. P. Murre, Reduction of the proof of the non-rationality of a non-singular cubic threefold to a result of mumford
  2. S. Bloch, J. P. Murre, On the Chow group of certain types of Fano threefolds
  3. Luciana Picco Botta, Alessandro Verra, The non rationality of the generic Enriques' threefold
  4. Allen B. Altman, Steven L. Kleiman, Foundations of the theory of Fano schemes
  5. Chad Schoen, On Hodge structures and non-representability of Chow groups
  6. Arnaud Beauville, Variétés de Prym et jacobiennes intermédiaires
  7. Noriyuki Suwa, Sur l'image de l'application d'Abel-Jacobi de Bloch

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