On the Chow group of certain types of Fano threefolds

S. Bloch; J. P. Murre

Compositio Mathematica (1979)

  • Volume: 39, Issue: 1, page 47-105
  • ISSN: 0010-437X

How to cite


Bloch, S., and Murre, J. P.. "On the Chow group of certain types of Fano threefolds." Compositio Mathematica 39.1 (1979): 47-105. <http://eudml.org/doc/89415>.

author = {Bloch, S., Murre, J. P.},
journal = {Compositio Mathematica},
keywords = {Fano threefolds; Chow group; Prym varieties; polarized intermediate Jacobian; rational equivalence; Abel-Jacobi map},
language = {eng},
number = {1},
pages = {47-105},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {On the Chow group of certain types of Fano threefolds},
url = {http://eudml.org/doc/89415},
volume = {39},
year = {1979},

AU - Bloch, S.
AU - Murre, J. P.
TI - On the Chow group of certain types of Fano threefolds
JO - Compositio Mathematica
PY - 1979
PB - Sijthoff et Noordhoff International Publishers
VL - 39
IS - 1
SP - 47
EP - 105
LA - eng
KW - Fano threefolds; Chow group; Prym varieties; polarized intermediate Jacobian; rational equivalence; Abel-Jacobi map
UR - http://eudml.org/doc/89415
ER -


  1. [1] S.S. Abhyankar: Resolution of singularities of embedded algebraic surfaces. Academic Press, New York1966. Zbl0147.20504MR217069
  2. [2] W. Barth, and A. Van De Ven: Lines on hypersurfaces, Archiv der Math.31 (1978) 96-104. Zbl0383.14003MR510081
  3. [3] A. Beauville: Variétés de Prym et jacobiennes intermédiaires. Ann. Scient. de l'Ecole Norm. Sup.10 (1977) 304-392. Zbl0368.14018MR472843
  4. [4] S. Bloch: An example in the theory of algebraic cycles, in Algebraic K-theory, Evanston 1976, Lect. Notes in Math. No. 551, 1-30, Springer Verlag, Heidelberg1976. Zbl0358.14003MR480504
  5. [5] S. Bloch: Torsion algebraic cycles and a theorem of Roitman, (to appear in Comp. Math.). Zbl0463.14002MR539002
  6. [6] W.-L. Chow: On the quotient variety of an abelian variety. Proc. Nat. Acad. Sci. U.S.A.38 (1952), 1039-1044. Zbl0049.38701MR52156
  7. [7] C.H. Clemens and P.A. Griffiths: The intermediate jacobian of the cubic threefold, Annals of Math.95 (1972), 281-356. Zbl0214.48302MR302652
  8. [8] F. Enriques: Sopra una involuzione non razionale dello spazio, Rend. Acc. Lincei (5a) 21 (1912), 81-83. JFM43.0702.01
  9. [9] P.A. Griffiths: Periods of integrals on algebraic manifolds I, II, Amer. J. of Math.90 (1968), 568-626, 805-865. Zbl0183.25501
  10. [FGA] A. Grothendieck: Fondements de la Géométrie Algébrique, Séminaire Bourbaki1957-62, Secrét. Math., Paris1962. Zbl0239.14002MR146040
  11. [SGA 1] A. Grothendieck: Séminaire de Géométrie Algébrique 1, Lecture Notes in Math.224, Springer-Verlag, Heidelberg1971. Zbl0234.14002
  12. [SGA 4] A. Grothendieck, M. Artin and J.L. Verdier: Séminaire de Géométrie Algébrique 4, Lecture Notes in Math.305, Springer-Verlag, Heidelberg1973. Zbl0245.00002MR354654
  13. [10] S.L. Kleiman: Algebraic cycles and the Weil conjectures, in Dix exposés sur la cohomologie des schémas, 359-386, North-Holland, Amsterdam1968. Zbl0198.25902MR292838
  14. [11] S. Lang: Abelian varieties, Interscience Publ.New York1959. Zbl0098.13201MR106225
  15. [12] D. Lieberman: Intermediate jacobians, in Algebraic Geometry Oslo 1970, 125-141, Wolters-Noordhoff, Groningen1972. Zbl0249.14015MR424832
  16. [13] D. Mumford: Abelian varieties, Oxford Univ. Press, Oxford1970. Zbl0223.14022
  17. [14] D. Mumford: Prym varieties I, in Contributions to Analysis, a collection of papers dedicated to L. Bers, 325-350, Academic Press, New York1974. Zbl0299.14018MR379510
  18. [15] D. Mumford: Algebraic Geometry I, Complex projective varieties, Grundlehren221, Springer-Verlag, Heidelberg1976. Zbl0356.14002MR453732
  19. [16] J.P. Murre: Algebraic equivalence modulo rational equivalence on a cubic threefold, Comp. Math.25 (1972), 161-206. Zbl0242.14002MR352088
  20. [ 17] J.P. Murre: Reduction of the proof of the non-rationality of a non-singular cubic threefold to a result of Mumford, Comp. Math.27 (1973), 63-82. Zbl0271.14020MR352089
  21. [18] J.P. Murre: Some results on cubic threefolds, in Classification of algebraic varieties and compact complex manifolds, Lect. Notes in Math. No 412, 140-164, Springer-Verlag, Heidelberg1974. Zbl0299.14019MR374145
  22. [19] J.P. Murre: On a uniqueness theorem for certain kinds of birational transformations, Indag. Math.21 (1959), 129-134. Zbl0098.34401MR118720
  23. [20] A.A. Roitman: Private correspondence. 
  24. [21] L. Roth: Algebraic threefolds, Ergeb. der Math., Neue Folge, Heft 6, Springer-Verlag, Heidelberg1955. Zbl0066.14704MR76426
  25. [22] P. Samuel: Rational equivalence of algebraic cycles, Amer. J. of Math.78 (1956), 383-400. Zbl0075.16002MR95845
  26. [23] B.R. Tennison: On the quartic threefold, Proc. London Math. Soc. (3) 29 (1974), 714-734. Zbl0308.14005MR419453
  27. [24] A.N. Tjurin, Five lectures on three dimensional varieties, Russian Math. Surveys27 (1972), 1-53. Zbl0263.14012MR412196
  28. [25] (added) V.A. Iskovskih: Fano 3-fold I (resp. II), Izvestija A.N. SSSR, Ser. Matem.41 (1977) 516-562 (resp. ibid.42 (1978) 506-549)= Math. of the USSR, Izvestije11 (1977) 485-527 (resp. forthcoming). Zbl0382.14013

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.