Log Crepant Birational Maps and Derived Categories

By Y. Kawamata. 2003

90 citations recorded by the source corpus.

We extend the conjecture on the derived equivalence and K-equivalence to the logarithmic case and prove it in the toric case.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8b0dd4fa8c8af6ba3f6755769bc1442ca39c33b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Motivic integration over Deligne–Mumford stacks (2003, background): “ivalent, that is, there are a smooth DM stack Y and proper birational morphisms fi: Y → Xisuch that f∗ 1 (KX1 +D1) ∼ f∗ 2 (KX2 +D2). Then we have an equation Σ(X1,D1) = Σ(X2,D2). Remark 1.5. Kawamata [8] obtained a closely related result in terms of the derived category. As an example of consequence”
Derived categories of coherent sheaves (2006, background): “Secondly, a special case of Kawamata’s work [27] on the effect of toroidal flips and flops on derived categories is the following result.”
Derived categories of toric varieties III (2006, result): “The proofs of the above statements are the same as in [15], [16] and [18] except Theorem 1 (a).”
On the conjecture of King for smooth toric Deligne-Mumford stacks (2008, result): “Another reason not to consider the nef case in this article is that the work of Kawamata [10] assures that the derived category of a nef del Pezzo toric stack is equivalent to that of the corresponding K-equivalent del Pezzo toric stack obtained by only keeping the vertices of Δ.”
Dirichlet Branes and Mirror Symmetry (2009, background): “86 has also been established as an equivalence of derived categories for finite subgroups G ⊂ Sp(n,C) by KaledinBezrukavnikov [45] and for finite abelian subgroups G ⊂ SL(n,C) by Kawamata [301].”
Stability conditions and extremal contractions (2012, methodology): “This result was generalized by Bridgeland [10] for arbitrary three dimensional flops, and by Kawamata [20] for toroidal cases.”
Phases Of N=2 Theories In 1+1 Dimensions With Boundary (2008, background): “A different construction of derived equivalences in the general multi-graded case had been given by Kawamata in [78].”