For general quartic double solids, two varieties are isomorphic if and only if their Kuznetsov components are equivalent, without assuming the equivalence has Fourier-Mumford type.
Calabi-Yau and fractional Calabi-Yau categories
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abstract
We discuss Calabi-Yau and fractional Calabi-Yau semiorthogonal components of derived categories of coherent sheaves on smooth projective varieties. The main result is a general construction of a fractional Calabi-Yau category from a rectangular Lefschetz decomposition and a spherical functor. We give many examples of application of this construction and discuss some general properties of Calabi-Yau categories.
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2019 1verdicts
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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
For general quartic double solids, two varieties are isomorphic if and only if their Kuznetsov components are equivalent, without assuming the equivalence has Fourier-Mumford type.