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
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- Helix Structures in Quantum Cohomology of Fano Varieties
- Cycles, derived categories, and rationality
- Motives and the Pfaffian-Grassmannian equivalence
- New examples of rational Gushel-Mukai fourfolds
- Categorical cones and quadratic homological projective duality
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- On the Chow ring of Fano varieties on the Fatighenti-Mongardi list
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- Derived categories of nodal del Pezzo threefolds
- Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces
- Special cubic birational transformations of projective spaces
- Frobenius and spherical codomains and neighbourhoods
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