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Responsabili:

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

Evento

Titolo: Rational cubic fourfolds containing a plane with nontrivial Clifford invariant
Quando: 22/05/2013 - 16:00
Dove: Palazzo Campana - TORINO
Aula: Aula Magna
Relatore: Michele Bolognesi
Afferenza: Université de Rennes I
Locandina:

Descrizione:

In this talk I will showcase a general class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. Equivalently, the Brauer class B of the even Clifford algebra over the discriminant cover (a K3 surface S of degree 2) associated to the quadric bundle, is nontrivial. These fourfolds provide nontrivial examples verifying Kuznetsov's conjecture on the rationality of cubic fourfolds containing a plane. Indeed, using homological projective duality for grassmannians, one obtains another K3 surface S' of degree 14 and a nontrivial twisted derived equivalence $A_{X}=D^{b}(S^{b},\beta)=D^{b}(S',\beta)$ , where $A_{X}$is Kuznetsov's residual category associated to the cubic hypersurface X.

Sede

Sede:
Indirizzo: Via Carlo Alberto n.10
CAP: 10123
Città: TORINO