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

claire.voisin@college-de-france.fr

photo
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Je suis aussi rattachée à l'IMJ-PRG

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


claire.voisin@imj-prg.fr


                                            
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Renaissance d'un  journal:  JEP  (Journal de l'Ecole polytechnique)


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Séminaire de géométrie algébrique de Jussieu

Séminaire  ``Autour des cycles algébriques''



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Journaux

Enseignement à l'X

2018- 2019  Enseignement  au Collège de France: 

Invariants birationnels

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



 

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Monographie:  Chow rings, decomposition of the diagonal  and the topology of families
Annals of Math. Studies 187,  Princeton University Press 201
4.

Chow et citrouille (par Enrico  Arbarello)



Recherche:
(Pré)publications récentes :

- Chow rings and gonality of general abelian varietiesarXiv:1802.07153

- Segre classes of tautological bundles on Hilbert schemes of surfaces , arXiv:1708.06325,  à paraître dans Algebraic Geometry.


- (avec J. Kollár, R. Laza et G. Saccà) Remarks on degenerations of hyper-Kähler manifolds, preprint 2017.


- (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 caseà paraître dans le volume de Contemporary Mathematics en l'honneur de Lawrence Ein.

Torsion points of sections of Lagrangian torus fibrations and the Chow ring of hyper-Kähler manifolds,
à paraître dans les proceedings de Abel symposium 2017.


- (avec Radu Laza  et Giulia Saccà)  A hyper-Kähler compactification of the Intermediate Jacobian fibration associated to 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:

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




Roquebrune






Famille 2010



Famille   1998-2014


Famille 2016