Michele Bolognesi, "Mutations on derived categories of conic bundles"

Together with M.Bernardara, a couple of years ago, we showed a criterion for rationality of conic bundles (on rational surfaces) purely in terms of dimensions of categorical representability. Roughly speaking: such a conic bundle is rational if and only if a SOD of its derived category contains only derived categories of algebraic varieties of dimension < 2.

One direction of the proof is made up by a study of semiorthogonal decompositions of all such rational conic bundles, which are classified by their discriminant loci. These are obtained by a combination of classical algebraic geometry and mutations on the SOD. In this talk I will discuss and detail some of these examples.