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- W4300773921 abstract "A classical result of Bondal-Orlov states that a standard flip in birational geometry gives rise to a fully faithful functor between derived categories of coherent sheaves. We complete their embedding into a semiorthogonal decomposition by describing the complement. As an application, we can lift the quadratic Fano correspondence (due to Galkin-Shinder) in the Grothendieck ring of varieties between a smooth cubic hypersurface, its Fano variety of lines, and its Hilbert square, to a semiorthogonal decomposition. We also show that the Hilbert square of a cubic hypersurface of dimension at least 3 is again a Fano variety, so in particular the Fano variety of lines on a cubic hypersurface is a Fano visitor. The most interesting case is that of a cubic fourfold, where this exhibits the first higher-dimensional hyperkahler variety as a Fano visitor." @default.
- W4300773921 created "2022-10-04" @default.
- W4300773921 creator A5031580580 @default.
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- W4300773921 date "2020-02-12" @default.
- W4300773921 modified "2023-09-24" @default.
- W4300773921 title "Derived categories of flips and cubic hypersurfaces" @default.
- W4300773921 doi "https://doi.org/10.48550/arxiv.2002.04940" @default.
- W4300773921 hasPublicationYear "2020" @default.
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