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
claire.voisin@imj-prg.fr
RIP
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Séminaire
de géométrie algébrique de Jussieu
Séminaire
``Autour des cycles algébriques''
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Journaux
Un nouveau journal: Moduli
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Enseignement au Collège de France 2016-2020 (vidéos)
Cours de géométrie algébrique 2006-2007 (notes)
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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 :
- On the Chow ring of very general abelian varieties and a question of Pirola, arXiv:2607.07053
- Unboundedness of zero-cycles on higher dimensional Fano manifolds,
arXiv:2511.23080
- Rank $2$ vector bundles and degrees of points of del Pezzo surfaces,
J. Reine Angew. Math. 2026, no. 836, (bicentennial issue 2026), 303–327.
- Varieties with representable CH0-group and a question of Colliot-Thélène , Algebraic Geometry 12 (6) 888-901, (2025), (volume en l'honneur de Gerard van der Geer).
- Universally defined cycles I,
Indag. Math. (N.S.) 37 (2026), no. 1, 376–398, (volume dédié à la mémoire de Jacob Murre).
- (avec O. Benoist) On the smoothability problem with rational coefficients,
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 36 (2025), no. 3, 393–408, (volume en l'honneur d'Enrico Bombieri).
-(avec J. Kollár) Flat pushforwards of Chern classes and the smoothability of cycles below the middle dimension, Annals of Math, Volume 200, Issue 2, 771-797 (2024).
- On Chern classes of Lagrangian fibered hyper-Kähler manifolds, PAMQ, Volume 21, Number 3 (volume dedicated to the memory of Jean-Pierre Demailly), 1393-1435, (2025).
- (avec A. Beauville, A. Etesse, A. Höring et J. Liu) Symmetric
tensors on the intersection of two quadrics and Lagrangian
fibration, Moduli 1, (2024).
- Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map, PAMQ, Volume 20, Number 5 (volume in honour of Enrico Arbarello), pp. 2469-2496 (2024) .
- Geometric representability of 1-cycles on rationally connected threefolds, dans Perspectives on four decades of Algebraic Geometry : in Memory of Alberto Collino, Progress in Mathematics,
volume 352, 467–492.
- (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
, 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).
- (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,
- (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.
Textes d'exposition:
- La conjecture de Hodge pour les variétés abéliennes de dimension au plus 5, d'après Markman. Séminaire Bourbaki 78ème année, 2025-2026, Exposé N°1248.
(NB.
Cet article a été refusé par Arxiv pour la raison qu'il est
écrit en français. This paper has been rejected by Arxiv because it is
written in French.)
- Hodge and generalized Hodge conjectures, coniveau and algebraic cycles, JOURNAL OF OPEN MATHEMATICAL PROBLEMS, 1(1):16–51, (2025).
- (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
CV en anglais
Arnaud Beauville
(mon
ancien directeur de thèse)
Mes étudiants
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Evaluer la biodiversité grâce aux
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L'orme de Gorbio
Famille 1998-2014
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