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# Nori's variety and its singularities.

Lundi, 16 Avril, 2007 - 12:30
Prénom de l'orateur :
Roland
Nom de l'orateur :
OLBRICHT
Résumé :

The moduli space of representations of a fixed dimension $n ge 2$ of the free associative algebra is a singular algebraic variety.
M.V. Nori has developed an approach to desingularise it. For
n=2, Nori's construction yields indeed a desingularization. We
will describe its homology and the structure of the fibres of the
desingularisation morphism. For n>2, Nori's variety is no longer
smooth. To understand its singularities, we study inside the variety
of all n^2-dimensional algebras the orbit closure of the algebra of
nxn matrices under the action of GL(n^2). For n = 3 we
will determine the singular locus of this orbit closure.

Institution de l'orateur :
Université de Munster
Thème de recherche :
Algèbre et géométries
Salle :
04