Derived categories of cubic fourfolds
Alexander Kuznetsov
TL;DR
This paper explores the structure of derived categories for specific cubic fourfolds and examines their connection to the rationality problem in algebraic geometry.
Contribution
It provides a detailed analysis of derived categories for Pfaffian, plane-containing, and singular cubic fourfolds, linking these structures to rationality questions.
Findings
Derived categories vary among different types of cubic fourfolds.
Connections established between derived category structures and rationality.
Insights into how singularities influence the derived category structure.
Abstract
We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.
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