Rational maps between varieties associated to central simple algebras

2016/02/14 by Novaković, Saša
#14E05 #16H05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.04444

Abstract

In this paper we show that if two central simple k-algebras generate the same cyclic subgroup in Br(k), then there are rational maps between varieties associated to these algebras, such as Brauer--Severi varieties, norm hypersurfaces and symmetric powers. In some cases we even have rational embeddings. We also relate the obtained results to the Amitsur conjecture.

Related

• A geometric perspective on Amitsur's conjecture
• Rationally connected varieties
• Bounds of the number of rational maps between varieties of general type
• Birational isomorphisms between generalized Severi-Brauer varieties
• Glider Brauer-Severi varietes of central simple algebras