Derived Categories of Cubic Fourfolds

By Alexander Kuznetsov. 2008

232 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/902597053e205bf0eda7b45e2e186b20da8a5f3e

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

On two rationality conjectures for cubic fourfolds (2014, background): “[11] A. Kuznetsov, Derived categories of cubic fourfolds.”
A categorical invariant for cubic threefolds (2009, methodology): “The main evidence for Conjecture 1.2 is that, in [ 17 ], it has been verified for all the basic examples of rational cubic fourfolds: the Pfaan cubics, the cubic fourfolds containing a plane described in [9] and the singular cubics.”
Derived Categories View on Rationality Problems (2015, background): “An appropriate sequence of mutations (see [K10]) then identifies the categories AX and D(S,B0).”
On the derived category of the classical Godeaux surface (2012, background): “Recently (see, for example, [32], [17], [22]) a number of results as well as conjectures try to link semi-orthogonal decompositions in derived categories to the birational geometry of X, including very subtle features such as the rationality or irrationality of X which do not seem to be detected by ”
Lectures on K3 Surfaces (2016, background): “It has been introduced by Kuznetsov in [343] and studied quite a lot, as it seems to be related to the rationality question for cubic fourfolds.”