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Calabi-Yau and fractional Calabi-Yau categories

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arxiv 1509.07657 v2 pith:CRCQDO7S submitted 2015-09-25 math.AG

Alexander Kuznetsov This is my paper · ORCID
classification math.AG
keywords calabi-yaucategoriesfractionalconstructiondiscussgeneralapplicationcategory
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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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  1. Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

    math.AG 2019-08 conditional novelty 6.0 of 10

    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.

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