Claire Voisin
Collège de France
3 rue d'Ulm
75005 Paris
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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ERC Synergy Grant HyperK 2020-2026 (avec O. Debarre, E. Macrì et D. Huybrechts)
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Séminaire
de géométrie algébrique de Jussieu
Séminaire
``Autour des cycles algébriques''
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Journaux
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2019- 2020 Enseignement au Collège de France:
Variations infinitésimales de structure de Hodge
Mon cours aura lieu le jeudi de 10h à 12h.
Premier cours le 27 février 2020.
Le cours a été interrompu mi-mars par
le confinement mais les trois dernières séances de cours seront filmées
à la maison et vont être mises en ligne sur le site du Collège de France d'ici la fin avril.
Enseignement au Collège de France (vidéos)
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Monographie: Chow rings, decomposition of the diagonal and the topology of
families,
Annals of Math. Studies 187, Princeton University Press
2014.
Chow et citrouille (par Enrico Arbarello)
Recherche:
(Pré)publications plus ou moins récentes :
- Schiffer variations and the generic Torelli theorem for hypersurfaces, arXiv:2004.09310
- Appendice à l'article de Giulia Saccà
Birational geometry of the intermediate Jacobian fibration of a cubic fourfold
arXiv:2002.01420
- 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 Junliang Shen et Qizheng Yin Topology of Lagrangian Fibrations and
Hodge Theory of Hyper-Kähler Manifolds
- 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 Arxiv arXiv:1810.11848
- 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,
- (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, arXiv: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'Grady, Recent 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) .
- 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).
- 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
CV en anglais
Arnaud Beauville
(mon
ancien directeur de thèse)
Mes étudiants
La Corse vue de Menton
Roquebrune
Famille 2010
Famille 1998-2014
Famille 2019