Equivalences of derived catgories of sheaves on smooth stacks
By Y. Kawamata. 2004
87 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2b3649e9ca637c6752c2c73e01025601b4e0461b
How researchers see this paper
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In Geometry and Topology
- Emanuele Macrì
- P. Stellari
- Arend Bayer
- Alberto Canonaco
- D. Huybrechts
- Chunyi Li
- David Ploog
- Yukinobu Toda
In Mathematical Physics
- Emanuele Macrì
- P. Stellari
- Arend Bayer
- Alberto Canonaco
- D. Huybrechts
- David Ploog
- Yukinobu Toda
- Y. Kawamata
Citations in the corpus
- The space of stability conditions on the local projective plane (2009, methodology): “0, for all p6= 0 and all 0 l n0. To extend to all Wk we use Beilinson’s resolutions in P2 (pulled-back toXk) and [ Kaw04 , Lemma 6.4].”
- A categorical invariant for cubic threefolds (2009, unknown): “exact triangle Km[m] −→ O• m −→ I ′, for Km := ker(Om m → Om−1 m ) ∈ Coh(Y′ × F(Y′)), splits. Hence O• m has a (unique) convolution I′ ⊕Km[m]. (For general facts about convolutions, see, for example, [6, 14, 23].) Consider the complex R• m:= {R(O Y′(−N ))⊕nm ⊠(L−rm)⊕sm −→ ··· −→ R(O ′(−N0))⊕n0 ⊠(L−r”
- Twisted Fourier–Mukai functors (2006, methodology): “As a consequence, we will observe that also the hypotheses in Kawamata’s result ([11]) can be weakened (see Remark 4.1).”
- Derived Categories of Toric Varieties (2005, methodology): “(5) follows from a similar generalization of the Beilinson resolution theorem ([1]) as in [11] §5.”
- Equivariant autoequivalences for finite group actions (2005, background): “This has been extended by Kawamata to smooth stacks associated to normal projective varieties with quotient singularities [11].”
- A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “on the functor A TOUR ABOUT EXISTENCE AND UNIQUENESS OF DG ENHANCEMENTS AND LIFTS 31 in [15]. A generalization of Orlov’s result to smooth stacks, which are obtained as global quotients, is proved in [28]. (2) The singular case: In [41], the case of projective (non-necessarily smooth) schemes is tre”
- Derived categories of toric varieties III (2006, background): “nly abelian quotient singularities. Moreover there exist only finitely many such birational maps when Xis fixed and Y is varied. Proof. Let E∈Db(X×Y) bethe kernel ofΦ, anobject givingthe equivalence Φ ([3]). Then we have an isomorphism E⊗p∗ 1ωX ∼= E⊗p∗ 2ωY where p1 and p2 are projections. Let T be the”