Derived categories of cyclic covers and their branch divisors

• Alexander Kuznetsov ^[1] ; Alexander Perry ^[2]
  1. [1] Independent University of Moscow

     Independent University of Moscow

     Rusia

     
  2. [2] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 389-423
• Idioma: inglés
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• Resumen

  • 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 Db(X) and Db(Z) with distinguished components AX and AZ and prove the equivariant category of AX (with respect to an action of the nth roots of unity) admits a semiorthogonal decomposition into n − 1 copies of AZ . As examples, we consider quartic double solids, Gushel–Mukai varieties, and cyclic cubic hypersurfaces.