On equivalences of derived and singular categories

• Autorzy: Vladimir Baranovsky , Jeremy Pecharich
• Języki publikacji: EN

Abstrakty

EN

Let X and Y be two smooth Deligne-Mumford stacks and consider a pair of functions f: X → $$ \mathbb{A}^1 $$, g:Y → $$ \mathbb{A}^1 $$. Assuming that there exists a complex of sheaves on X × $$ \mathbb{A}^1 $$ Y which induces an equivalence of D b(X) and D b(Y), we show that there is also an equivalence of the singular derived categories of the fibers f −1(0) and g −1(0). We apply this statement in the setting of McKay correspondence, and generalize a theorem of Orlov on the derived category of a Calabi-Yau hypersurface in a weighted projective space, to products of Calabi-Yau hypersurfaces in simplicial toric varieties with nef anticanonical class.

Słowa kluczowe

EN

Derived category; Singular category; Landau-Ginzburg model; McKay correspondence

Kategorie tematyczne

• 14B05: Singularities

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 1-14

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Vladimir Baranovsky

• UC-Irvine

autor

Jeremy Pecharich

• UC-Irvine

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0063-y