Liste de publications

Articles de recherche


  1. Footnotes to papers of O'Grady and Markman, Mathematische Zeitschrift volume 300,   (volume en l'honneur d'Olivier Debarre), pages 3405–3416 (2022).
  2. Compact Kähler manifolds with no projective specialization,  Boll. Unione Mat. Ital. 15 (2022), no. 1-2  (volume en l'honneur de F. Catanese), 353–364.
  3. Schiffer variations and the generic Torelli theorem for hypersurfaces,  Compositio Mathematica , Vol. 158 , Issue 1  (2022) , pp. 89 - 122.
  4. On the Lefschetz standard conjecture for Lagrangian covered  hyper-Kähler varieties,   Advances in Mathematics 396 (2022).
  5.  (avec Olivier Debarre, Frédéric Han et Kieran O’Grady)  Hilbert squares of K3 surfaces and Debarre-Voisin varieties, Journal de l'Ecole polytechnique, Tome 7 (2020), p. 653-710.
  6.  Chow rings and gonality of general abelian varieties , Annales Henri Lebesgue 1 (2018) 313-332.
  7. Segre classes of tautological bundles on Hilbert schemes of surfaces , Algebraic Geometry 6 (2) (2019) 186–195.
  8.  (avec J. Kollár, R. Laza et G. Saccà) Remarks on degenerations of hyper-Kähler manifolds, Annales de l'Institut Fourier,  Tome 68, no 7 (2018), p. 2837-2882.
  9. Hyper-Kähler compactification of  the intermediate Jacobian fibration of a cubic fourfold : the twisted case,  Local and global methods in algebraic geometry, 341-355, Contemp. Math., 712, Amer. Math. Soc., Providence, RI, 2018.
  10. Torsion points of sections of Lagrangian torus fibrations and the Chow ring of hyper-Kähler manifolds,
    The Abel Symposium  Abelsymposium 2017: Geometry of Moduli,  pp 295-326 .
  11. (Avec Radu Laza et Giulia Saccà)   A hyper-Kähler compactification of the Intermediate Jacobian fibration associated with  a cubic fourfold,  Acta Mathematica, 218:1 (2017),  55-135.
  12. On the universal $CH_0$ group of cubic hypersurfaces  JEMS Volume 19, Issue 6 (2017) pp. 1619-1653
  13. (Avec K. Ranestad)  Variety of power sums and divisors in the moduli space of cubic fourfolds,     Documenta Mathematica 22 (2017), 455-504.
  14. (avec Bert van Geemen)  On a conjecture of Matsushita,  Int Math Res Notices (2016) Vol. 2016, 3111-3123.
  15. Remarks and questions on coisotropic subvarieties and 0-cycles of hyper-Kähler varieties,   dans  “K3 Surfaces and Their Moduli”, Proceedings of the Schiermonnikoog conference 2014, C. Faber, G. Farkas, G. van der Geer, Editors, Progress in Math 315,  Birkhäuser (2016), 365-399.
  16. Some new   results on  modified diagonals, Geometry & Topology 19-6 (2015), 3307--3343.
  17. Unirational threefolds with no universal  codimension $2$ cycle, Inventiones mathematicae: Volume 201, Issue 1 (2015), Page 207-237.
  18. The generalized Hodge  and Bloch conjectures  are equivalent for  general complete intersections, II,  J. Math. Sci. Univ. Tokyo  22 (2015), 491–517.
  19. Rational equivalence of $0$-cycles on $K3$ surfaces and  conjectures of Huybrechts and O'Grady,  Recent Advances in Algebraic Geometry, éditeurs C. Hacon, M. Mustaþã et M. Popa, London Mathematical Society Lecture Notes Series 417, Cambridge University Press, 422-436  (2015). 
  20.  Approximately rationally or elliptically connected varieties, Proceedings of the Edinburgh Mathematical Society (Series 2) , Volume  57, Issue 1 (in honour of Shokurov),   281 - 297  ( 2014) .
  21. Bloch's conjecture for Catanese and Barlow surfaces, J. Differential Geometry 97 (2014) 149-175.
  22. Infinitesimal invariants for cycles modulo  algebraic equivalence and $1$-cycles on Jacobians, Algebraic Geometry 2 (2014) 140-165.
  23. (avec O. Debarre et Z. Jiang)  Pseudo-Effective Classes and Pushforwards, Pure and Applied Mathematics Quarterly Volume 9, Number 4 (Special Issue: In memory of Andrey Todorov)  643—664, (2013).
  24. Remarks on curve classes on rationally  connected varieties, Clay Mathematics Proceedings  Volume 18,  591-599 (2013). 
  25. The generalized Hodge and Bloch conjectures are equivalent for general complete intersections,  Annales scientifiques de l'ENS 46, fascicule 3 (2013), 449-475.
  26. Abel-Jacobi map, integral Hodge classes and  decomposition of the diagonal, J. Algebraic Geom. 22 (2013), 141-174.
  27. Symplectic involutions of $K3$ surfaces act  trivially on $CH_0$, Documenta Math. 17 (2012) 851--860.
  28. Degree 4  unramified cohomology with finite coefficients and torsion codimension  3 cycles,  in Geometry and Arithmetic, (C. Faber, G. Farkas, R. de Jong Eds),
    Series of Congress Reports, EMS, 347-368 (2012) .
  29. (avec Jean-Louis Colliot-Thélène)  Cohomologie non ramifiée et conjecture de Hodge entière,    Duke Math. Journal, Volume 161, Number 5, 735-801 (2012).
  30. Chow rings and  decomposition theorems for  families of  $K3$ surfaces and Calabi-Yau hypersurfaces,  Geometry & Topology 16 (2012) 433–473.
  31.  (Avec O. Debarre, L. Ein, R. Lazarsfeld)  Pseudoeffective and nef classes on  abelian varieties,  Compositio Mathematica, Volume 147, pp 1793 - 1818  (2011).
  32. (avec Andreas Höring)   Anticanonical divisors and curve classes on Fano manifolds,  Pure and Applied Mathematics Quarterly, Volume 7, Number 4 (Special Issue: In memory of Eckart Viehweg), 1371-1393 (2011).
  33. (Avec O. Debarre)  Hyper-Kähler fourfolds and Grassmann geometry,  J. reine angew. Math. 649 (2010), 63-87. Correction.
  34. Coniveau  2 complete intersections  and effective cones, Geom. Funct. Anal. Vol. 19 (2010) 1494–1513.
  35. Rationally connected  $3$-folds and symplectic geometry, dans Géométrie  différentielle, Physique mathématique,  Mathématiques et société  (II),  Volume en l'honneur de Jean Pierre Bourguignon (O. Hijazi, éd.), Astérisque 322 (2008).
  36. (Avec E. Amerik)  Potential density of rational points on the variety  of lines of a cubic fourfold, Duke Math. Journal, Vol 145, n0 2,  379-408,  (2008).
  37. Hodge structures on cohomology algebras and geometry,  Math. Ann. 341 (2008), no. 1, 39--69 ,  article
  38. On the Chow ring of certain algebraic hyper-Kähler manifolds, Pure and Applied Mathematics Quarterly, Volume 4, Number 3, (Special issue in honor of Fedya Bogomolov) , 2008 . résumé , article.
  39. Hodge loci and absolute Hodge classes,  Compositio Mathematica, Vol. 143 Part 4, 945-958, 2007.  résumé, article.
  40. On integral Hodge classes on uniruled and Calabi-Yau threefolds,  in {\it Moduli Spaces and Arithmetic Geometry}, Advanced Studies in Pure Mathematics 45, 2006, pp. 43-73.  résumé, article.
  41. On the homotopy type of Kähler manifolds and the birational Kodaira problem, J. Differential Geom. 72 (2006), no. 1, 43--71. résumé, article.
  42. A generalization of the Kuga-Satake construction, Pure and Applied Mathematics Quarterly, Volume 1, Number 3 (Special Issue: In memory of Armand Borel, Part 2 of 3) 415-439, 2005. résumé, article .
  43. (Avec C. Soulé) Torsion cohomology classes and algebraic cycles on complex projective manifolds, Advances in Mathematics, Special volume in honor of Michael Artin, Part I, Vol 198/1 pp 107-127 (2005).  résumé, article
  44. Green's canonical syzygy conjecture for generic curves of odd genus,  Compos. Math. 141 (2005), no. 5, 1163--1190. MR2157134  résumé, article.
  45. On the homotopy types of compact Kähler and complex projective manifolds,   Inventiones  Math. Volume 157, Number 2, (2004), 329 - 343.MR2076925 résumé, article.
  46.  A geometric application of Nori's connectivity theorem,  Annali della Scuola Norm. Sup. di Pisa, Vol. III (2004), 637-656.MR2099253 résumé, article.
  47. Intrinsic pseudo-volume forms and K-correspondences,  Proceedings of the Fano Conference, (Eds A.Collino, A. Conte, M. Marchisio), Publication de l'Université de Turin (2004).MR2112602  résumé, article
  48. Remarks on filtrations on Chow groups and the Bloch conjecture, Annali di matematica 183, 421-438 (2004). MR2082666 Abstract, article.
  49. (avec A. Beauville) On the Chow ring of a K3 surface,  J. Algebraic Geom. 13 (2004), no. 3, 417--426. MR2047674 , article
  50.  (avec M. Aprodu) Green-Lazarsfeld's conjecture for generic curves of large gonality , CRAS, Volume 336, Issue 4,  Pages 335-339, (2003).MR1976314  résumé, article
  51.  A counterexample to the Hodge conjecture extended to K\"ahler varieties, IMRN 2002, n0 20, 1057-1075. MR1902630 , article
  52. Green's conjecture for curves of even genus lying on a K3 surface, J.Eur. Math. Soc. 4, 363-404 (2002).MR1941089 , article
  53. Linear spaces contained in the secant variety of a projective curve, appendice \`a un article de Ch. Soulé, J. Algebraic Geom. 13 (2004), 343-347.MR2047702 , article.
  54.  Nori's connectivity theorem and higher Chow groups, Journal of the Inst. Math. Jussieu (2002) 1 (2), 307-329.MR1954824  Abstract, article
  55.  On the punctual Hilbert scheme of a symplectic fourfold, Volume en l'honneur de  Herb Clemens, Contemporary   Mathematics, Vol; 312, (2002).MR1941585  .
  56. On the Hilbert scheme of an almost complex fourfold, Annales de l'Institut Fourier Tome 50 (2000), fascicule 2, 689-722.MR1775365  Abstract, article
  57. The Griffiths group of a general Calabi-Yau threefold is not finitely generated,  Duke Math. J. Vol. 102, No 1 (2000), 151-186.MR1741781, article
  58. Some results on Green's higher Abel-Jacobi map, Annals of Math. 149 , 451-473 ( 1999). MR1689335 , article
  59. A  generic Torelli theorem for the quintic threefold,dans New trends in Algebraic Geometry,  édité par Hulek, Catanese, Peters et Reid, Lond. Math. Soc. Lecture Note Series 264. MR1714833 ,
  60. (avec L. Bonavero) Schémas de Fano et variétés de Moishezon , C.R. Acad. Sci. Paris, t. 323 serie 1 , 1019-1024. (1996).MR1423213 ,.
  61.  Sur les groupes de Chow de certaines hypersurfaces, C. R. Acad. Sci.Paris, t. 322, serie 1, 73-76, 1996. MR1390824  .
  62.  On a conjecture of Clemens on rational curves on hypersurfaces Journal of Differential Geometry 44 (1996) 200-214, article, MR1420353 + Correction :  J. Differential Geom. 49 (1998), no. 3, 601--611. MR1669712 , article
  63. A mathematical proof of  a formula of Aspinwall and Morrison, Compositio Mathematica 104,135-151,1996.MR1421397  .
  64.  Remarks on zero-cycles of self-products of varieties,  dans Moduli of vector bundles (Proceedings du congrès  Taniguchi sur les fibrés vectoriels), édité par Maruyama, Decker (1994) 265-285.MR1397993  , article
  65. Une preuve élémentaire de la trivialité du groupe CH_0 d'une surface d'Enriques,  dans  Algebraic geometry  , édité par P. Newstead, Decker 1998.MR1651107 .
  66. Variations de structure de Hodge et zéro-cycles sur les surfaces générales,  Mathematische Annalen 299, 77-103 (1994).MR1273077  , article
  67. Sur l'application d'Abel-Jacobi des variétés de Calabi-Yau de dimension trois,  Annales de l'ENS,4eme série, tome 27 (1994) 209-226.MR1266470  , article
  68.  Miroirs et involutions sur les surfaces K3,dans  Journées de géométrie algébrique d'Orsay, juillet 92, édité par A. Beauville, O. Debarre, Y. Laszlo, Astérisque 218 (1993) 273-323. MR1265318 , article
  69.  Déformation des syzygies et théorie de Brill-Noether,  Proc. London Math. Soc. 3 ,vol. 67 (1993) 493-515. MR1238043 .
  70. Densité du lieu de Noether-Lefschetz pour les sections hyperplanes des variétés de Calabi-Yau de dimension trois, International Journal of Mathematics , vol. 3, N0 5 (1992) 699-715.MR1189682  .
  71.  Structure de Hodge mixte sur certains groupes d'homotopie et application d'Abel-Jacobi,  Topology vol. 32 N0 2, 395-417 (1993).  MR1217077, article
  72.  Une approche infinitésimale du théorème de H. Clemens sur les cycles d'une quintique générale de P^4, J. Algebraic geometry 1,(1992), 157-174.MR1129844  , article
  73. Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme, Annali della Scuola Normale Superiore di Pisa, Serie 4, vol. 19 (1992) 473-492. MR1205880  , article
  74.  Sur la stabilité des sous-variétés lagrangiennes des variétés symplectiques holomorphes, publié dans: Complex projective geometry, proceedings de la conférence de Trieste, juin
    89, édité par Ellingsrud,Peskine,Sacchiero et Stromme, London Math. Soc. Lecture notes series 179, 294-302.MR1201391  , article
  75.  Sur l'application de Wahl des courbes satisfaisant la condition de Brill-Noether-Petri, Acta Mathematica , vol. 168 (1992) 249-272. MR1161267 , Full paper
  76. Contrexemple \`a une conjecture de Harris,  C.R.A.S. Paris, t.313, Série 1, 685-687 (1991). MR1135439  ,  article
  77.  Sur le lieu de Noether-Lefschetz en degré 6 et 7, Compo. Mathematica 75 (1990) 47-68.MR1059955  , article
  78.  Dégénérations de Lefschetz et variations de structure de Hodge,  J. of Differential Geometry 31 (1990) 527-534.MR1037413  ,  article
  79. Relations dans l'anneau de Chow de la surface des coniques des variétés de Fano, Amer. J. of Mathematics 112 (1990) 877-898.MR1081809  , Full paper
  80.  Sur une conjecture de Griffiths et Harris, publié dans: Algebraic curves and projective geometry, Proceedings Trento 1988, E. Ballico, C. Ciliberto Eds, Lecture Notes in Mathematics N0 1389, 270-275.  MR1023405 .
  81.   Une remarque sur l'invariant infinitésimal des fonctions normales, C.R.A.S. Paris, t.307, Série 1, 157-160 (1988). MR0956607 , article
  82.  Courbes tétragonales et cohomologie de Koszul, J. Reine Angew. Math. 387 (1988). MR0946352 , article
  83. Composantes de petite codimension du lieu de Noether-Lefschetz, Comment. Math. Helvetici (1989) 515-526. article,  MR1022994 ,
  84. Une précision concernant le théorème de Noether, Math. Annalen 280, 605-611, (1988). MR0939921  , article.
  85. Sur la jacobienne intermédiaire du double solide d'indice deux, abstract Duke Math. Journal Vol.57, (1988), 629-646. MR0962523 , article
  86. Théorème de Torelli pour les cubiques de P^5, Invent. Math. 86, 577-601(1986), article.  MR0860684 ,   Correction, Invent. Math. 172 (2008), no. 2, 455--458


ARTICLES DE SYNTHESE ET NOTES DE COURS




  1. Birational invariants and decomposition of the diagonal ,  dans   Birational geometry of hypersurfaces, Eds. A. Hochenegger, M. Lehn, P. Stellari, Lecture Notes of the Unione Matematica Italiana 26, Springer, pp. 3-71  (2019).
  2. Hodge structures, coniveau and algebraic cycles, dans The Legacy of Bernhard Riemann After One Hundred and Fifty Years , Editors: Lizhen Ji, Frans Oort, Shing-Tung Yau  Advanced Lectures of Mathematics ,No.: 35, Higher Education Press (Beijing)  International Press (Boston).
  3. The Hodge conjecture. Open problems in mathematics, 521-543, Springer,  (2016).
  4. Chow rings, decomposition of the diagonal  and the topology of families,  Annals of Math. Studies 187, Princeton University Press 2014.
  5. Hodge loci, in  Handbook of moduli  (Eds G. Farkas and I. Morrison), Advanced Lectures in Mathematics 25, Volume III, International Press, 507-547 (2013).
  6. On the Cohomology of Algebraic Varieties,  Proceedings of the International Congress of Mathematicians 
    (Hyderabad, India, 2010),  Vol. I, 476-503.
  7.  Sections rationnelles de fibrations sur les surfaces et conjecture de Serre (d'après de Jong, He et Starr),  Séminaire BOURBAKI,   volume  2010-2011, exposé no 1038, p. 317-337, Astérisque 348, Société Mathématique de France  (2012).
  8. Algebraic geometry versus Kähler geometry,   Milan J. Math. 78 (2010), no. 1, 85–116.  Article
  9. Géométrie des espaces de modules de courbes et de surfaces K3, d'après Gritsenko-Hulek-Sankaran, Farkas-Popa, Mukai, Verra, Séminaire Bourbaki  2006/2007,  Exposé 981, Société Mathématique de France., Astérisque 317, 467-490 (2008).
  10. Cohomology algebras in symplectic, Kähler and algebraic  geometry,    Proceedings de ICCM 2007, vol 2, article.
  11. Some aspects of the Hodge conjecture,    Japan. J. Math. 2, 261-296 (2007) article.
  12. Recent progresses in Kaehler and complex projective geometry,  Laptev, A. (ed.),  European congress of mathematics  (ECM), Stockholm,  Sweden, June 27--July 2, 2004. Zürich: European Mathematical Society (2005). Abstract, article
  13. On some problems of Kobayashi and Lang ; algebraic approaches,  Current Developments in Mathematics 2003, no. 1 (2003), 53–125 ,MR2132645 article
  14. Théorie de Hodge et géométrie algébrique complexe , Cours spécialisés 10,
    SMF 2002. Traduction Hodge Theory and complex  algebraic geometry I and II, Cambridge University Press 2002-3.MR1967689 MR1997577
  15. Variations of Hodge structure of Calabi-Yau threefolds, Publication de la scuola Normale superiore di Pisa, 1998.MR1658398
  16.  Symétrie miroir, Panoramas et syntheses , 1996.MR1396787 MR1711184
  17. Transcendental methods in the study of algebraic cycles, dans    Algebraic cycles and Hodge theory, Cours du C.I.M.E. , Lecture Notes in Mathematics 1594, Springer verlag (1994), 153-222. Article  MR1335241
  18. Variations of Hodge structure and algebraic cycles , Proceedings of the international congress of mathematicians , Zürich, (1994). article  ,   MR1403971