Derived categories of toric varieties III

By Y. Kawamata. 2006

130 citations recorded by the source corpus.

We prove that the derived McKay correspondence holds for the cases of finite abelian groups and subgroups of $$\mathrm{GL}(2,\mathbf {C})$$GL(2,C). We also prove that K-equivalent toric birational maps are decomposed into toric flops.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f56e2f30e38caa8c9a888692c6af0fc4e28b814e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quantum Cohomology and Periods (2011, methodology): “ to remove the factor (−2πz)−n/2 there to redeﬁne these ingredients. 30 HIROSHI IRITANI This holds true in our case because X does not have generic stabilizers and we can apply the result of Kawamata [41] that the derived category Db(X) of coherent sheaves has a full exceptional collection {E}N i=1.”
Convergence of quantum cohomology by quantum Lefschetz (2005, background): “emisimple if its bounded derived category Db coh (X) of coherent sheaves admits a full exceptional collection. In fact, Kawamata recently showed that toric varieties have full exceptional collections [21]. For the application of the main theorem 1.1, we need to know the convergence of big quantum co”
On the conjecture of King for smooth toric Deligne-Mumford stacks (2008, background): “ of the Grothendieck group of P , which is not a coincidence, but rather is expected by Remark 3.15. 10 LEV BORISOV AND ZHENG HUA Remark 5.3. The case of Picard number one has already been settled in [Ka], but we have treated it here nonetheless, to give a unied picture of our approach. We will now ”
Derived categories of coherent sheaves (2006, unknown): “preserves a complex symplectic form on Cn. Secondly, a special case of Kawamata’s work [26] on the eﬀect or toroidal ﬂips and ﬂops on derived categories is the following result. Theorem 2.7 (Kawamata [27]). Conjecture 2.5 holds when G is abelian. Note that in this case all resolutions are toric. Kaw”
The derived category of a GIT quotient (2012, methodology): “ extensions. It follows that w and <w are right t-exact on the category Db S (X). The following is an extension to our setting of an observation which appeared in [4], following ideas of Kawamata [17]. There the authors described semiorthogonal factors appearing under VGIT in terms of the quotien”
Projective toric varieties as fine moduli spaces of quiver representations (2006, background): “th a complete strong exceptional collection of line bundles, [BP] establishes that the variety is isomorphic to a connected component of a corresponding moduli space of stable quiver representations. [Kaw] proves that every toric variety has a complete exceptional collection of coherent sheaves and,”