Categorical representability and birational geometry - Michele Bolognesi (Université de Montpellier)

Abstract: In this talk we will first survey some ideas concerning the construction of possible birational invariants from semiorthogonal decompositions of the derived category of coherent sheaves on a given variety X. We will then introduce categorical representability, and show how in several cases it can give interesting indications on the rationality of the base variety X. In particular we will devolop the case of varieties that are fibered in intersection of quadrics, for example fibrations in del Pezzo quartics.