Motifs des fibrés en quadriques et jacobiennes intermédiaires relatives des paires K3-Fano

Abstract : This thesis consists of two parts. In the first part we study the Chow motive of a quadric bundle of odd relative dimension over a surface. We show that this motive admits a decomposition which involves the Prym motive of the double covering of the discriminant curve.In the second part, we consider Lagrangian fibrations, obtained as relative intermediate Jacobians of families of Fano threefolds containing a fixed K3 surface, and the existence of a symplectic compactification. In a particular case, we study a partial compactification using calculations with the software system Macaulay2.
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Johann Bouali. Motifs des fibrés en quadriques et jacobiennes intermédiaires relatives des paires K3-Fano. Géométrie algébrique [math.AG]. Université de Bourgogne, 2015. Français. ⟨NNT : 2015DIJOS021⟩. ⟨tel-01244646⟩

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