2013/08/03 by Schillewaert, Jeroen, Van Maldeghem, Hendrik
#14M12 #17C37 #20G15 #51A45 #51E24 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1308.0745
Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e.~the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in 8-di\-men\-sional projective spaces, the line Grassmannians in 14-dimensional projective spaces, and the exceptional varieties of type E6 in 26-dimensional projective space. Our theorem can be regarded as a far-reaching generalization of Mazzocca and Melone's approach to finite quadric Veronesean varieties. This approach takes projective properties of complex Severi varieties as smooth varieties as axioms.