Calabi-Yau and fractional Calabi-Yau categories

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.

24 pages, v2: minor corrections

References in corpus (2)

• Küchle fivefolds of type c5
• On Küchle manifolds with Picard number greater than 1

Cited by in corpus (13)

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• Categorical Torelli theorems for Gushel-Mukai threefolds
• A note on spherical functors
• Semi-Calabi-Yau orbifolds and mirror pairs
• Universal functors on symmetric quotient stacks of Abelian varieties
• On the Chow groups of Plücker hypersurfaces in Grassmannians
• Derived categories of quartic double fivefolds
• On two families of Enriques categories over K3 surfaces