A categorical invariant for cubic threefolds

By M. Bernardara, Emanuele Macrì, Sukhendu Mehrotra, P. Stellari. 2009

80 citations recorded by the source corpus.

We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism class.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fdb4dc09825229457cd3b75caa023fa037e27b6b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stability conditions on Kuznetsov components (2017, background): “t needed for our construction, it may be useful to compare stable objects in Db(X) versus stable objects in Ku(X), in a similar fashion as what has been done in [LMS15, Section 3]. More precisely, in [BMMS12], the Kuznetsov component Ku(Y3) is realized as an admissible subcategory in Db(P2,B0) ortho”
Fano varieties of cubic fourfolds containing a plane (2009, background): “(Y) := H4(Y,Z) ∩H2,2(Y) = hH2,Pi, where, for simplicity, we denote by H2 the self-intersection of the ample line bundle OY (H). It is easy to see that a very generic Y satisﬁes (∗) (see, for example, [5] and Remark 2.3). Corollary3.5. If Y is very generic, then there exists a birational morphism F(Y”
Instanton bundles on Fano threefolds (2012, methodology): “We would also like to mention that this approach to the description of the category BY3 was used in [2].”