1998/10/09 by Emilia Mezzetti, Mezzetti, Emilia, Dario Portelli +1
Mathematics · #14C20 #14J30 #14M07 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C20 #msc:14J30 #msc:14M07 #msc:14M20
paper · pdf · doi:10.48550/arxiv.math/9810057
26 pages, to appear on Mathematische Nachrichten
arxiv created 1998/10/09 · arxiv updated 2009/11/30
It is known that the smooth rational threefolds of P5 having a rational non-special surface of P4 as general hyperplane section have degree d=3,... ,7. We study such threefolds X from the point of view of linear systems of surfaces in P3, looking in each case fosr an explicit description of a birational map from P3 to X. For d=3,..., 6 we prove that there exists a line L on X such that the projection map of X centered at L is birational; we completely describe the base loci B of the linear systems found in this way and give a description of any such threefold X as a suitable blowing-down of the blowing-up of P3 along B. If d=7, i.e. if X is a Palatini scroll, we prove that, conversely, a similar projection never exists.