Projective homogeneous varieties birational to quadrics

2009/03/22 by MacDonald, Mark L.
#11E04 (Primary) 14E05 #14C15 (Secondary) #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0903.3698

Abstract

We will consider an explicit birational map between a quadric and the projective variety X(J) of traceless rank one elements in a simple reduced Jordan algebra J. X(J) is a homogeneous G-variety for the automorphism group G=Aut(J). We will show that the birational map is a blow up followed by a blow down. This will allow us to use the blow up formula for motives together with Vishik's work on the motives of quadrics to give a motivic decomposition of X(J).

Related

• Motives of unitary and orthogonal homogeneous varieties
• Blowups and fibers of morphisms
• On special quadratic birational transformations of a projective space
• Critical varieties and motivic equivalence for algebras with involution
• Birational Transformations on Irreducible Compact Hermitian Symmetric Spaces