Derived categories and rationality of conic bundles.

Marcello Bernardara (1) , Michele Bolognesi (2)

1 Fakultät für Mathematik
2 IRMAR - Institut de Recherche Mathématique de Rennes

We show that a standard conic bundle over a minimal rational surface is rational and its Jacobian splits as the direct sum of Jacobians of curves if and only if its derived category admits a semiorthogonal decomposition by exceptional objects and the derived categories of those curves. Moreover, such a decomposition gives the splitting of the intermediate Jacobian also when the surface is not minimal.

Domaines: Géométrie algébrique [math.AG]

Marcello Bernardara, Michele Bolognesi. Derived categories and rationality of conic bundles.. 2010. ⟨hal-00525711v2⟩