2005/01/18 by Raf Bocklandt, Bocklandt, Raf, Stijn Symens +3
Mathematics · #14B05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B05
paper · pdf · doi:10.48550/arxiv.math/0501270
24 pages. Added missing reference. Made clear that throughout the paper we only work with smooth orders
arxiv created 2005/01/27 · arxiv updated 2009/12/01
Given a Cayley-Hamilton smooth order A in a central simple algebra Σ, we determine the flat locus of the Brauer-Severi fibration of the smooth order. Moreover, we give a classification of all (reduced) central singularities where the flat locus differs from the Azumaya locus and show that the fibers over the flat, non-Azumaya points near these central singularities can be described as fibered products of graphs of projection maps, thus generalizing an old result of Artin on the fibers of the Brauer-Severi fibration over a ramified point. Finally, we show these fibers are also toric quiver varieties and use this fact to compute their cohomology.