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Communication Dans Un Congrès Année : 2005

Varieties of reductions for $gl_n$

Laurent Manivel

Résumé

We study the varieties of reductions associated to the variety of rank one matrices in $\fgl_n$. These varieties are defined as natural compactifications of the different ways to write the identity matrix as a sum of $n$ rank one matrices. Equivalently, they compactify the quotient of $PGL_n$ by the normalizer of a maximal torus. In particular, we prove that for $n=4$ we get a $12$-dimensional Fano variety with Picard number one, index $3$, and canonical singularities.
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Dates et versions

hal-00003975 , version 1 (20-01-2005)

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Atanas Iliev, Laurent Manivel. Varieties of reductions for $gl_n$. Projective varieties with unexpected properties, Jun 2004, Sienne, Italy. pp.287-316. ⟨hal-00003975⟩

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