# Categorical representability and intermediate Jacobians of Fano threefolds

• ### Marcello Bernardara

Université Paul Sabatier, Toulouse, France
• ### Michele Bolognesi

Université de Montpellier, France

A subscription is required to access this book chapter.

## Abstract

We define, basing upon semiorthogonal decompositions of ${\rm D}^{\rm b}(X)$, categorical representability of a projective variety $X$ and describe its relation with classical representabilities of the Chow ring. For complex threefolds satisfying both classical and categorical representability assumptions, we reconstruct the intermediate Jacobian from the semiorthogonal decomposition. We discuss finally how categorical representability can give useful information on the birational properties of $X$ by providing examples and stating open questions.