Varieties of reductions for $gl_n$
Iliev, Atanas ; Manivel, Laurent
HAL, hal-00003975 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-06-08
Classification:  abelian matrix algebra,  reduction,  Fano variety,  14J45; 20G20; 14L30,  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] 
@article{hal-00003975,
     author = {Iliev, Atanas and Manivel, Laurent},
     title = {Varieties of reductions for $gl\_n$},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003975}
}

Iliev, Atanas; Manivel, Laurent. Varieties of reductions for $gl_n$. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003975/