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Fourier-Mukai transforms for quotient varieties. (English) Zbl 1387.14059

As noticed in the footnote of the beginning, this article is the largely unedited version of the manuscript appeared on the arXiv in 1998 [arXiv:math/9811101]. In this paper derived equivalences for smooth projective varieties with finite-order canonical bundles. The main result is Theorem 4.5, which says that any such equivalence has a lift to Fourier-Mukai transforms between the canonical covers. Applying this statement to the surface case, several new derived equivalences are constructed for minimal projective surfaces, namely for Enriques surfaces and bielliptic surfaces.

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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References:

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