Liste de publications
Articles de recherche
- Footnotes to papers of O'Grady and Markman, Mathematische Zeitschrift
volume 300, (volume en l'honneur d'Olivier Debarre), pages 3405–3416 (2022).
- 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.
- Schiffer variations and the generic Torelli theorem for hypersurfaces, Compositio Mathematica
,
Vol. 158
,
Issue 1 (2022) , pp. 89 - 122.
- On the Lefschetz standard conjecture for Lagrangian covered hyper-Kähler varieties, Advances in Mathematics 396 (2022).
- (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.
- Chow rings and gonality of general abelian varieties
, Annales Henri Lebesgue 1 (2018) 313-332.
- Segre classes of tautological bundles on Hilbert schemes of surfaces , Algebraic Geometry 6 (2) (2019) 186–195.
- (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.
- 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.
- 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 .
- (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.
- On the universal $CH_0$ group of cubic hypersurfaces JEMS Volume 19, Issue 6 (2017) pp. 1619-1653
- (Avec K. Ranestad) Variety of power sums and divisors in the moduli space of cubic fourfolds, Documenta Mathematica 22 (2017), 455-504.
- (avec Bert van Geemen) On a conjecture of Matsushita, Int Math Res Notices (2016) Vol. 2016, 3111-3123.
- 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.
- Some new results on modified diagonals, Geometry & Topology 19-6 (2015), 3307--3343.
- Unirational threefolds with no universal codimension $2$ cycle, Inventiones mathematicae: Volume 201, Issue 1 (2015), Page 207-237.
- The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II, J. Math. Sci. Univ. Tokyo
22 (2015), 491–517.
- 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).
- 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) .
- Bloch's conjecture for Catanese and Barlow surfaces, J. Differential Geometry 97 (2014) 149-175.
- Infinitesimal invariants for cycles modulo algebraic equivalence and $1$-cycles on Jacobians, Algebraic Geometry 2 (2014) 140-165.
- (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).
- Remarks on curve classes on rationally connected varieties, Clay Mathematics Proceedings Volume 18, 591-599 (2013).
- The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, Annales scientifiques de l'ENS 46, fascicule 3 (2013), 449-475.
- Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal, J. Algebraic Geom. 22 (2013), 141-174.
- Symplectic involutions of $K3$ surfaces act trivially on $CH_0$, Documenta Math. 17 (2012) 851--860.
- 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) .
- (avec Jean-Louis Colliot-Thélène) Cohomologie non ramifiée et conjecture de Hodge entière, Duke Math. Journal, Volume 161, Number 5, 735-801
(2012).
- Chow rings and decomposition theorems for families of $K3$ surfaces and Calabi-Yau hypersurfaces, Geometry & Topology 16 (2012)
433–473.
- (Avec O. Debarre, L. Ein, R. Lazarsfeld) Pseudoeffective and nef classes on abelian
varieties, Compositio Mathematica, Volume 147, pp 1793 - 1818 (2011).
- (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).
- (Avec O. Debarre) Hyper-Kähler fourfolds and Grassmann geometry, J. reine angew. Math. 649 (2010), 63-87. Correction.
- Coniveau 2 complete intersections and effective cones, Geom. Funct. Anal. Vol. 19 (2010) 1494–1513.
- 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).
- (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).
- Hodge structures on cohomology algebras and geometry, Math. Ann. 341 (2008), no. 1, 39--69 , article
- 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.
- Hodge loci and absolute Hodge classes, Compositio
Mathematica, Vol. 143 Part 4, 945-958, 2007. résumé, article.
- 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.
- On the homotopy type of Kähler manifolds and the
birational
Kodaira problem, J.
Differential Geom. 72 (2006),
no. 1,
43--71. résumé, article.
- 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 .
- (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
- Green's canonical syzygy conjecture for generic curves of odd
genus, Compos.
Math. 141 (2005), no.
5, 1163--1190. MR2157134
résumé, article.
- On the homotopy
types of compact Kähler and complex projective
manifolds, Inventiones
Math. Volume 157, Number 2, (2004), 329 - 343.MR2076925
résumé, article.
- A geometric application of Nori's connectivity
theorem, Annali della Scuola Norm. Sup. di Pisa, Vol. III (2004),
637-656.MR2099253
résumé, article.
- 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
- Remarks on filtrations on Chow groups and the Bloch conjecture,
Annali di matematica 183, 421-438 (2004). MR2082666
Abstract, article.
- (avec A. Beauville) On the Chow ring of a K3 surface, J.
Algebraic Geom. 13 (2004), no.
3, 417--426. MR2047674 , article
- (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
- A counterexample to the Hodge conjecture extended to
K\"ahler varieties, IMRN 2002, n0 20, 1057-1075. MR1902630 , article
- Green's conjecture for curves of even genus lying on a K3
surface, J.Eur. Math. Soc. 4, 363-404 (2002).MR1941089 , article
- 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.
- Nori's connectivity theorem and higher Chow groups, Journal
of the Inst. Math. Jussieu (2002) 1 (2), 307-329.MR1954824
Abstract, article
- On the punctual Hilbert scheme of a symplectic fourfold,
Volume en
l'honneur de Herb Clemens, Contemporary Mathematics, Vol;
312,
(2002).MR1941585 .
- On the Hilbert scheme of an almost complex fourfold, Annales de
l'Institut Fourier Tome 50 (2000), fascicule 2, 689-722.MR1775365
Abstract, article
- 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
- Some results on Green's higher Abel-Jacobi map, Annals of Math.
149 , 451-473 ( 1999). MR1689335 , article
- 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
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- (avec L. Bonavero) Schémas de Fano et variétés de Moishezon ,
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- Sur les groupes de Chow de certaines hypersurfaces, C.
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hypersurfaces Journal of Differential Geometry 44 (1996) 200-214, article, MR1420353
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- Une preuve élémentaire de la trivialité du groupe CH_0 d'une
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- Variations de structure de Hodge et zéro-cycles sur les
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- Miroirs et involutions sur les surfaces K3,dans
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- Déformation des syzygies et théorie de Brill-Noether,
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- Densité du lieu de Noether-Lefschetz pour les sections
hyperplanes des variétés de Calabi-Yau de dimension trois,
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- Une approche infinitésimale du théorème de H. Clemens sur
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- Sur la stabilité des sous-variétés lagrangiennes des
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ARTICLES DE SYNTHESE ET NOTES DE COURS
- 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).
- 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).
-
The Hodge conjecture.
Open problems in mathematics,
521-543, Springer, (2016).
- Chow rings, decomposition of the diagonal and the topology of families, Annals of Math. Studies 187, Princeton University Press 2014.
- Hodge loci, in Handbook of moduli (Eds G. Farkas and I. Morrison), Advanced Lectures in Mathematics 25, Volume III, International Press, 507-547 (2013).
- On the Cohomology of Algebraic Varieties, Proceedings of the International Congress of Mathematicians
(Hyderabad, India, 2010), Vol. I, 476-503.
- Sections rationnelles de fibrations sur les surfaces et conjecture de Serre
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- Algebraic geometry versus Kähler geometry, Milan J. Math. 78 (2010), no. 1, 85–116. Article
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Mukai, Verra, Séminaire Bourbaki
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