Derived categories of cyclic covers and their branch divisors

2014/11/30 by Alexander Kuznetsov, Alexander Perry · 1 citation
Mathematics · #Action (physics) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cover (algebra) #Decomposition #Degree (music) #Divisor (algebraic geometry) #Equivariant map #Homotopy and Cohomology in Algebraic Topology #Variety (cybernetics) #math.AG

paper · pdf · doi:10.1007/s00029-016-0243-0

published as Selecta Math, V. 23 (2017), N. 1, pp. 389--423 · 27 pages, minor changes

arxiv created 2015/12/17 · openalex publication_date 2016/05/02 · openalex created_date 2016/06/24 · arxiv updated 2018/09/05 · openalex updated_date 2026/08/05

Abstract

Given a variety Y with a rectangular Lefschetz decomposition of its derived category, we consider a degree n cyclic cover X → Y ramified over a divisor Z ⊂ Y. We construct semiorthogonal decompositions of D^b(X) and D^b(Z) with distinguished components A_X and A_Z, and prove the equivariant category of A_X (with respect to an action of the n-th roots of unity) admits a semiorthogonal decomposition into n-1 copies of A_Z. As examples we consider quartic double solids, Gushel-Mukai varieties, and cyclic cubic hypersurfaces.

Citations

• Cohomological descent theory for a morphism of stacks and for equivariant derived categories

Cited by

• Calabi–Yau and fractional Calabi–Yau categories