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On equivalences of derived and singular categories

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Baranovsky V., Pecharich J.

Open Mathematics

2010

tom 8

nr 1

1-14

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.

Ograniczanie wyników

1 Open Mathematics

1 Baranovsky V.

1 Pecharich J.

1 2010

Wyniki wyszukiwania

On equivalences of derived and singular categories