Claire Voisin
  Directrice de recherche au CNRS,
Institut de Mathématiques de Jussieu-Paris rive gauche
Equipe Topologie et géométrie algébriques
4 Place Jussieu
Case 247
75252  Paris Cedex 05

(pour toute communication concernant ICM 2026 : )


ERC Synergy Grant HyperK 2020-2026 (avec O. Debarre, E. Macrì et  D. Huybrechts)

Séminaire de géométrie algébrique de Jussieu

Séminaire  ``Autour des cycles algébriques''

Géométrie algébrique
16-20 mai 2022 à l'IHP, à l'occasion de mes 60 ans.



Un nouveau journal:  Moduli

Enseignement  au Collège de France 2016-2020  (vidéos)

Cours de géométrie algébrique 2006-2007 (notes)

Monographie:  Chow rings, decomposition of the diagonal  and the topology of families
Annals of Math. Studies 187,  Princeton University Press 201

Chow et citrouille (par Enrico  Arbarello)

(Pré)publications plus ou moins récentes :

  -(avec J. Kollár)   Flat pushforwards of Chern classes and  the  smoothability of  cycles in the Whitney range, preprint  arXiv:2311.04714.

- On Chern classes of Lagrangian fibered hyper-Kähler manifolds, preprint arXiv:2305.09396 .

- (avec A. Beauville, A. Etesse, A. Höring et J. Liu)  Symmetric tensors on the intersection of two quadrics and  Lagrangian fibration, preprint arXiv:2304.10919.

- Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map, preprint  arXiv:2212.03046, à paraître au PAMQ, volume en l'honneur d'Enrico Arbarello.

- Geometric representability of 1-cycles on rationally  connected threefolds, preprint     arXiv:2208.12557, à paraître dans Perspectives on four decades: Algebraic Geometry 1980—2020. In memory of Alberto Collino, Birkhäuser.

- (avec O. Debarre, D. Huybrechts, E. Macrì Computing Riemann-Roch polynomials and classifying  hyper-Kähler fourfolds,   J. Amer. Math. Soc. 37 (2024), no. 1, 151-185.

On   fibrations and measures of irrationality  of hyper-Kähler manifolds
, Revista de la Unión Matemática Argentina Vol. 64, No. 1, 2022, (special volume MCA) Pages 165–197.

- (avec G. Oberdieck et J. Song)   Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds,
Pure and Applied Mathematics Quarterly Volume 18 (in honour of Herb Clemens), Number 4, 1723–1748, 2022.

-  Footnotes to papers of O'Grady and Markman, Mathematische Zeitschrift volume 300  (2022),  (volume en l'honneur d'Olivier Debarre), 3405–3416.

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.

- On the coniveau of rationally connected threefolds , arXiv:2010.05275, Geometry & Topology 26 (2022) 2731–2772.

On the Lefschetz standard conjecture for Lagrangian covered  hyper-Kähler varieties,   Advances in Mathematics 396 (2022), Paper No. 108108, 29 pp.

Schiffer variations and the generic Torelli theorem for hypersurfaces Compositio Mathematica ,Volume 158, Issue 1, pp. 89 - 122 (2022).

- Appendice à l'article de Giulia Saccà  Birational geometry of the intermediate Jacobian fibration of a cubic fourfold

- Appendice à l'article de Soheyla Feyzbakhsh, Richard P. Thomas An application of wall-crossing to Noether-Lefschetz loci, arXiv:1912.01644.

-  Appendice à l'article de E. Shinder Variation of Stable Birational Types of Hypersurfaces, arXiv:1903.02111 

-  (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.

- Triangle varieties and surface decomposition of hyper-Kähler manifolds in Recent Developments in Algebraic Geometry: To Miles Reid for his 70th Birthday,  edited by Hamid Abban; Gavin Brown; Alexander Kasprzyk; Shigefumi Mori, London Mathematical Society Lecture Note Series 478, Cambridge University Press (2022), 315-356.

- 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.

- (avec E. Colombo, G. Farkas, A. Verra)  Syzygies of Prym and paracanonical curves of genus 8, Epijournal de Géométrie Algébrique, Volume 1 (2017), Article Nr. 7.

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 varietiesarXiv:1501.02984,  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.

- The generalized Hodge  and Bloch conjectures  are equivalent for  general complete intersections, II,  J. Math. Sci. Univ. Tokyo  22 (2015) (Kodaira Centennial issue), 491–517.

  -  Unirational threefolds with no universal  codimension $2$ cycle, Inventiones mathematicae: Volume 201, Issue 1 (2015), Page 207-237.

Textes d'exposition:

(Avec Mauro Varesco)   Hyper-Kähler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence. Milan J. Math. 90 (2022), no. 2, 433–444.

Birational invariants and decomposition of the diagonal ,  in Birational geometry of hypersurfaces, Eds. A. Hochenegger, M. Lehn, P. Stellari, Lecture Notes of the Unione Matematica Italiana 26, Springer, pp. 3-71  (2019).

The Hodge conjecture. Open problems in mathematics, 521-543, Springer,  (2016).

Hodge Structures, Coniveau and Algebraic Cycles, in The Legacy of Bernhard Riemann After One Hundred and Fifty Years, ALM35, Higher Education Press and International Press, Beijing–Boston, pp. 719–745 (2016).

-   Stable birational invariants and the Lüroth problem,  Surveys in Differential Geometry XXI, International Press 2016.

- Hodge loci, in  Handbook of moduli  (Eds G. Farkas and I. Morrison), Advanced Lectures in Mathematics 25, Volume III, International Press, 507-546.

Liste complète de publications


CV en anglais

Arnaud Beauville (mon ancien directeur de thèse)

Mes étudiants

La Corse vue de Menton


L'orme de Gorbio

Famille   1998-2014

Famille 2022

Une photo ironique  du catalogue de l'exposition Women of mathematics throughout Europe, A gallery of portrait  par Sylvie Paycha et Noel Tovia Matoff, photographe Noel Tovia Matoff