2003/06/23 by Atanas Iliev, Iliev, Atanas, Laurent Manivel +1
Computer Science · Mathematics · #14J45 #14M17 #14N05 #32M15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14J45 #msc:14M17 #msc:14N05 #msc:32M15
paper · pdf · doi:10.48550/arxiv.math/0306328
41 pages
arxiv created 2003/06/23 · openalex publication_date 2003/06/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the varieties of reductions associated to the four Severi varieties, the first example of which is the Fano threefold of index 2 and degree 5 studied by Mukai and others. We prove that they are smooth but very special linear sections of Grassmann varieties, and rational Fano manifolds of dimension 3a and index a+1, for a=1, 2, 4, 8. We study their maximal linear spaces and prove that through the general point pass exactly three of them, a result we relate to Cartan's triality principle. We also prove that they are compactifications of affine spaces.