Sur le théorème de Torelli pour les solides doubles quartiques

Olivier Debarre

Compositio Mathematica (1990)

  • Volume: 73, Issue: 2, page 161-187
  • ISSN: 0010-437X

How to cite


Debarre, Olivier. "Sur le théorème de Torelli pour les solides doubles quartiques." Compositio Mathematica 73.2 (1990): 161-187. <>.

author = {Debarre, Olivier},
journal = {Compositio Mathematica},
keywords = {double solid; codimension of the singular locus; theta-divisor; conic bundle; Prym variety; Torelli problem},
language = {fre},
number = {2},
pages = {161-187},
publisher = {Kluwer Academic Publishers},
title = {Sur le théorème de Torelli pour les solides doubles quartiques},
url = {},
volume = {73},
year = {1990},

AU - Debarre, Olivier
TI - Sur le théorème de Torelli pour les solides doubles quartiques
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 73
IS - 2
SP - 161
EP - 187
LA - fre
KW - double solid; codimension of the singular locus; theta-divisor; conic bundle; Prym variety; Torelli problem
UR -
ER -


  1. [B1] A. Beauville, Variétés de Prym et jacobiennes intermédiaires. Ann. Sc. Ecole Norm. Sup.10, (1977), 309-391. Zbl0368.14018MR472843
  2. [B2] A. Beauville, Prym varieties and the Schottky problem, Invent. Math.41, (1977), 149-196. Zbl0333.14013MR572974
  3. [B3] A. Beauville, Sous-variétés spéciales des variétés de Prym, Comp. Math.45, (1982), 357-383. Zbl0504.14022MR656611
  4. [C] H. Clemens, Double solids, Adv. in Math.47, (1983), 107-230. Zbl0509.14045MR690465
  5. [C-G] H. Clemens, P. Griffiths, The Intermediate Jacobian of the Cubic Threefold, Ann. of Math.95, (1972), 281-356. Zbl0214.48302MR302652
  6. [D1] O. Debarre, Sur les variétés de Prym des courbes tétragonales, Ann. Sc. Ec. Norm. Sup.21, (1988), 545-559. Zbl0674.14034MR982333
  7. [D2] O. Debarre, Sur le problème de Torelli pour les variétés de Prym, Am. J. of Math.111, (1989), 111-134. Zbl0699.14052MR980302
  8. [D3] O. Debarre, Sur les variétés abéliennes dont le diviseur thêta est singulier en codimension 3, Duke Math. J.56, (1988), 221-273. Zbl0699.14058MR952234
  9. [D4] O. Debarre, Variétés de Prym et ensembles d'Andreotti et Mayer. A paraître. Zbl0716.14029
  10. [D5] O. Debarre, Le théorème de Torelli pour les intersections de trois quadriques, Inv. Math.95, (1989), 507-528. Zbl0705.14029MR979362
  11. [Do] R. Donagi, The tetragonal construction, Bull. Amer. Math. Soc.4, (191), 181-185. Zbl0491.14016MR598683
  12. [D-S] R. Donagi, R. Smith, The structure of the Prym map, Acta Math.146, (1981), 25-102. Zbl0538.14019MR594627
  13. [F-L] W. Fulton, R. Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146, (1981), 271-283. Zbl0469.14018MR611386
  14. [H] J. Harris, Theta-characteristics on algebraic curves, Trans. A.M.S. 271, (1982), 611-638. Zbl0513.14025MR654853
  15. [Ha] R. Hartshorne, Complete intersections and connectedness, Amer. J. of Math.84, (1962), 497-508. Zbl0108.16602MR142547
  16. [K] Kanev, Quadratic singularities of the Pfaffian theta divisor of a Prym variety, Math. Notes of the Ac. of Sc. of the USSR, 31, (1982), 301-305. Zbl0568.14017
  17. [M1] D. Mumford, Prym Varieties I. Contributions to Analysis, Acad. Press, New York (1974), 325-350. Zbl0299.14018MR379510
  18. [M2] D. Mumford, On the Kodaira Dimension of the Siegel Modular Variety. Springer Lecture Notes 997, Springer Verlag, New York, (1983), 348-375. Zbl0527.14036MR714757
  19. [M3] D. Mumford, Theta characteristics of an algebraic curve, Ann. Sci. Ecole Norm. Sup.4, (1971), 181-192. Zbl0216.05904MR292836
  20. [S-V] R. Smith, R. Varley, Components of the locus of singular theta divisors in genus 5. In Algebraic Geometry, Sitges 1983, Springer Lecture Notes in Mathematics 1124, Springer Verlag (1985), 338-416. Zbl0598.14036
  21. [T] A. Tikhomirov, The Abel-Jacobi map of sextics of genus three on double spaces of P3 of index two. Soviet Math. Dokl.33, (1986), 204-206. Zbl0622.14032
  22. [V] C. Voisin, Sur la jacobienne intermédiaire du double solide d'indice deux. Duke Math. J.57, (1988), 629-646. Zbl0698.14049MR962523
  23. [W1] G. Welters, Abel-Jacobi isogenies for certain types of Fano threefold. Mathematical Centre Tracts 141, Math. Centrum, Amsterdam, (1981). Zbl0474.14028MR633157
  24. [W2] G. Welters, A theorem of Gieseker-Petri type for Prym varieties. Ann. Sci. Ecole Norm. Sup.18 (1985), 671-683. Zbl0628.14036MR839690
  25. [Z] S. Zucker, Generalized Intermediate Jacobians and the Theorem on Normal Functions, Inv. Math.33, (1976), 185-222. Zbl0329.14008MR412186

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.