Derived Categories View on Rationality Problems

By Alexander Kuznetsov. 2015

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/351417c00bc48662255ed77aed665c4f5339e330