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Responsabili:

Federica Galluzzi  ed  Elena Martinengo
 

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

Evento

Titolo: On the smoothness of the Nori-Hilbert scheme of associative algebras
Quando: 27/05/2015 - 16:30
Dove: Palazzo Campana - TORINO
Aula: Aula C
Relatore: Francesco Vaccarino
Afferenza: Politecnico di Torino
Locandina: Locandina

Descrizione:

Abstract :

The Nori-Hilbert scheme of an associative algebra A, which is a generalization of the usual Hilbert scheme of n-points of a commutative ring, can be considered as a litmus paper to test "smoothness" conditions satisfied by an associative algebra of low cohomological dimension. 

Indeed it is a classical result that the usual Hilbert scheme of n-points is smooth when computed over smooth quasi-projective curves or surfaces.
 
In this talks we will give some recents results concerning this problem, namely:
 
- the above scheme is smooth when the second Ext(M,M)=0 for all finite dimensional A-modules (this confirms what was known for finite dimensional algebras)
 
- the above scheme is in general not smooth for 2-Calabi Yau algebras (we will provide a counterexample by means of the group algebras of the fundamental group of topological surfaces of genus greater than one).
 
We will give a detailed description of the local geometry of the above in terms of Hochschild cohomology of A.
 
Joint works with Alessandro Ardizzoni, Raf Bocklandt and Federica Galluzzi
 

Sede

Sede: Palazzo Campana - Sito web
Indirizzo: Via Carlo Alberto 10
CAP: 10123
Città: TORINO