Projective bundles and blow-ups of Projective spaces

TL;DR

This paper explores the relationship between projective bundles over projective spaces and specific blow-ups of projective spaces, focusing on their geometric and algebraic properties.

Contribution

It provides new insights into the connection between these two classes of non-singular projective varieties of Picard rank 2.

Findings

Identifies conditions under which projective bundles and blow-ups are related.

Establishes a correspondence between certain projective bundles and blow-up varieties.

Enhances understanding of the structure of Picard rank 2 varieties.

Abstract

The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.