Morphisms to Brauer-Severi Varieties, with Applications to Del Pezzo Surfaces

TL;DR

This paper classifies morphisms from proper varieties to Brauer-Severi varieties, extending classical results, and applies these findings to study del Pezzo surfaces, rational points, and arithmetic properties.

Contribution

It introduces a classification of morphisms to Brauer-Severi varieties and applies this to analyze del Pezzo surfaces and related arithmetic phenomena.

Findings

Classified morphisms to Brauer-Severi varieties.

Recovered classical results on rational points and Hasse principle.

Provided new insights into weak approximation for del Pezzo surfaces.

Abstract

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.