Derived categories view on rationality problems
arXiv:1509.09115 · doi:10.1007/978-3-319-46209-7_3
Abstract
We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate Jacobian, and discuss its possible applications to the geometry of prime Fano threefolds and cubic fourfolds.
Lecture notes for the CIME-CIRM summer school, Levico Terme, June 22--27, 2015; 26 pages