Thèse soutenue

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Accès à la thèse
Auteur / Autrice : Qizheng Yin
Direction : Claire VoisinBen Moonen
Type : Thèse de doctorat
Discipline(s) : Mathématiques statistique
Date : Soutenance en 2013
Etablissement(s) : Paris 6

Mots clés

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Résumé

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Tautological classes are geometrically constructed classes of algebraic cycles. The geometry and enumerative properties of these classes are especially interesting. The first part of this thesis unifies two classical notions of tautological classes: one on the moduli space of curves (in the sense of Mumford, Faber, etc. ), and the other on the Jacobian of a curve (in the sense of Beauville, Polishchuk, etc. ). Following Polishchuk, we construct relations between tautological classes using the motivic structures of the Jacobian. With these relations, we obtain various consequences on the well-known conjectures of Faber. The second part is focused on detecting non-trivial tautological classes on the generic Jacobian. Using a degeneration argument due to Fakhruddin, we develop a simple invariant in this context. We detect non-trivial classes both in the Chow groups and in S. Saito's higher Griffiths groups. In particular, we obtain a new proof of a theorem of Green and Griffiths, as well as an improvement of a result of Ikeda.