Claire Voisin
 Collège de France
3 rue d'Ulm
75005 Paris

Je suis aussi rattachée à l'IMJ-PRG

  Institut de Mathématiques de Jussieu-Paris rive gauche
Equipe Topologie et géométrie algébriques


 Conférence The geometry of algebraic varieties

A conference on the occasion of Olivier Debarre's 60th birthday

September 30–October 4, 2019, in CIRM at Luminy

Séminaire de géométrie algébrique de Jussieu

Séminaire  ``Autour des cycles algébriques''



Enseignement à l'X


2018- 2019  Enseignement  au Collège de France: 

Invariants birationnels  (Notes)

Mon cours aura lieu le jeudi de 10h à 12h.  Premier cours le 9 mai 2019.


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 récentes :
-    (avec O. Debarre, F. Han, K. O'Grady)  Hilbert squares of K3 surfaces and Debarre-Voisin varieties

- Triangle varieties and surface decomposition of hyper-Kähler manifolds Arxiv   arXiv:1810.11848

- Chow rings and gonality of general abelian varietiesarXiv:1802.07153, à paraître aux Annales Henri Lebesgue.

- 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, à paraître aux Annales de l'Institut Fourier.

- (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.

- 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)  (2013), 643-664.

- Bloch's conjecture for Catanese and Barlow surfaces, J. Differential Geometry 97 (2014) 149-175.

- Rational equivalence of $0$-cycles on $K3$ surfaces and  conjectures of Huybrechts and O'GradyRecent Advances in Algebraic Geometry, éditeurs C. Hacon, M. Mustaţă et M. Popa, London Mathematical Society Lecture Notes Series 417, Cambridge University Press, 422-436  (2015). 

- Remarks on curve classes on rationally  connected varieties, Clay Mathematics Proceedings  Volume 18, 2013, 591-599.

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 2012, 347-368.

- The generalized Hodge and Bloch conjectures are equivalent for general complete intersections,  Annales scientifiques de l'ENS 46, fascicule 3 (2013), 449-475.

- Approximately rationally or elliptically connected varieties, Proceedings of the Edinburgh Mathematical Society (Series 2) , Volume  57, Issue 1 (in honour of Shokurov),
p 281 - 297  ( 2014) .

- (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.

Textes d'exposition:

Birational invariants and decomposition of the diagonal , Gargnano lecture notes (2018).

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/description des travaux

Arnaud Beauville (mon ancien directeur de thèse)

Mes étudiants

La Corse vue de Menton


Famille 2010

Famille   1998-2014

Famille 2016