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

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.

comments are welcome, revised version, some minor mistakes in the previous version is corrected and some new results are added