Francia's flip and derived categories
By Y. Kawamata. 2001
57 citations recorded by the source corpus.
We extend some of the results of Bondal-Orlov on the equivalence of derived categories to the case of orbifolds by using the category of coherent orbifold sheaves.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9d67148a61ad7e9a3dbea6aef5ba1fba3ceb661e
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In Geometry and Topology
- Y. Kawamata
- Yukinobu Toda
- T. Bridgeland
- Michel van den Bergh
- B. Totaro
- Alexander Kuznetsov
- P. Stellari
- Emanuele Macrì
In Mathematical Physics
- Yukinobu Toda
- Y. Kawamata
- T. Bridgeland
- Michel van den Bergh
- B. Totaro
- Emanuele Macrì
- P. Stellari
- Arend Bayer
Citations in the corpus
- Non-commutative Crepant Resolutions (2002, background): “The existence of an embedding/equivalence D(X) → D(X) was proved by Kawamata in [23] (in a slightly more general situation).”
- Relative integral functors for singular fibrations and singular partners (2006, unknown): “If we apply φ∗ to (4.1) we get the analogous formula (4.2) RHom•OY ′ (Φ ′ Zx(ωZx),Oy) ≃ RHom • OY ′ (Φ′Zx(OZx),RHom • OY ′ (Oy,OY ′))[m] , After shifting degrees if necessary, we can assume that H0(K′•Zx) 6= 0 and H i(K′•Zx) = 0 for i > 0.”
- Log Crepant Birational Maps and Derived Categories (2003, methodology): “This is a generalization of [ 4 ] Theorem 5.2.”
- Equivalences of derived catgories of sheaves on smooth stacks (2004, background): “Note that there are more sheaves on the stack X than the underlying variety X, and as was shown in [ 9 ], the correct category which should be considered is that of the stacky sheaves, not the ordinary sheaves.”
- Derived categories of coherent sheaves (2006, methodology): “Kawamata explained this using the example of the Francia flip [25].”
- The resolution property for schemes and stacks (2002, methodology): “It allows the hard-to-verify assumption of a Cohen-Macaulay global cover to be removed from various papers, such as Kawamata’s paper on ips and derived categories [ 19 ].”