2015/09/30 by Alexander Kuznetsov
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Coherent sheaf #Component (thermodynamics) #Decomposition #Derived category #Projective test #Proposition #Series (stratigraphy) #math.AG
paper · pdf · doi:10.1515/crelle-2017-0004
24 pages, v2: minor corrections
arxiv created 2016/04/15 · openalex created_date 2016/06/24 · openalex publication_date 2017/03/02 · arxiv updated 2018/09/05 · openalex updated_date 2026/08/05
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 applications of this construction and discuss some general properties of Calabi–Yau categories.