Morphisms to Brauer-Severi varieties, with applications to del Pezzo surfaces

Christian Liedtke

Published 2016-02-24Version 1

We classify morphisms from proper varieties to Brauer-Severi varieties, which generalizes the classical correspondence between morphisms to projective space and globally generated invertible sheaves. As an application, we study del Pezzo surfaces of large degree with a view towards Brauer-Severi varieties, and recover classical results on rational points, the Hasse principle, and weak approximation.