# Hyperplane sections of projective bundle associated to the tangent bundle of $\mathbb{P}^2.$

## TL;DR

This paper provides a comprehensive classification of hyperplane sections of the projective bundle related to the tangent bundle of al P^2, and explores their deformations within a specific algebraic variety.

## Contribution

It offers a complete description of hyperplane sections of the projective bundle over al P^2 and characterizes their deformations in the flag variety SL_3()/B.

## Key findings

- Classified all hyperplane sections of the projective bundle over al P^2.
- Described possible deformations of certain Schubert divisors within SL_3()/B.

## Abstract

In this note we give a complete description of all the hyperplane section of the projective bundle associated to the tangent bundle of $\mathbb{P}^2$ under its natural embedding in $\mathbb{P}^7.$ As an application one obtains a description of all possible deformations, in $\text{SL_3(\mathbb{C}}/B,$ of the co-dimension one sub-scheme which is the union of two fundamental Schubert divisors.