2005/01/20 by Atanas Iliev, Iliev, Atanas, Laurent Manivel +1
Mathematics · #14J45 #14L30 #20G20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14J45 #msc:14L30 #msc:20G20
paper · pdf · doi:10.48550/arxiv.math/0501329
arxiv created 2005/01/20 · openalex publication_date 2005/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.