Calabi-Yau and fractional Calabi-Yau categories
Alexander Kuznetsov
TL;DR
This paper introduces a method to construct fractional Calabi-Yau categories from geometric data and explores their properties, with numerous examples illustrating its broad applicability in algebraic geometry.
Contribution
It provides a new construction technique for fractional Calabi-Yau categories using Lefschetz decompositions and spherical functors, expanding the toolkit for studying derived categories.
Findings
Constructed fractional Calabi-Yau categories from geometric data
Provided multiple examples demonstrating the construction's versatility
Discussed general properties and implications of 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.
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