6533b834fe1ef96bd129d210

RESEARCH PRODUCT

Motives of quadric bundles and relative intermediate jacobians of K3-Fano pairs

Johann Bouali

subject

Quadric bundleMotif de ChowIntermediate Jacobian[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Variété symplectique irréductibleLagrangian fibrationChow motiveFibration LagrangienneJacobienne intermédiaireIrreducible symplectic varietyPaire K3-FanoFibré en quadriquesK3-Fano pair

description

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.

https://theses.hal.science/tel-01244646