Derived categories of cyclic covers and their branch divisors
By Alexander Kuznetsov, Alexander Perry. 2014
49 citations recorded by the source corpus.
Given a variety Y with a rectangular Lefschetz decomposition of its derived category, we consider a degree n cyclic cover $$X \rightarrow Y$$X→Y ramified over a divisor $$Z \subset Y$$Z⊂Y. We construct semiorthogonal decompositions of $$\mathrm {D^b}(X)$$Db(X) and $$\mathrm {D^b}(Z)$$Db(Z) with distinguished components $${\mathcal {A}}_X$$AX and $${\mathcal {A}}_Z$$AZ and prove the equivariant category of $${\mathcal {A}}_X$$AX (with respect to an action of the nth roots of unity) admits a semiorthogonal decomposition into $$n-1$$n-1 copies of $${\mathcal {A}}_Z$$AZ. As examples, we consider quartic double solids, Gushel–Mukai varieties, and cyclic cubic hypersurfaces.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0e244d70fcfb3c704ae614df2153d8f8e47ff5fe
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In Geometry and Topology
- Alexander Perry
- Alexander Kuznetsov
- K. Hori
- Emanuele Macrì
- P. Stellari
- Nicolas Addington
- I. Smith
- D. Huybrechts
In Mathematical Physics
- Alexander Perry
- Alexander Kuznetsov
- K. Hori
- Emanuele Macrì
- P. Stellari
- I. Smith
- David Tong
- T. Bridgeland
Citations in the corpus
- Derived categories of Gushel–Mukai varieties (2016, result): “Similarly, the results of [31] show that odd GM categories can be described as “quotients” of even GM categories by involutions.”