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

Abstract

The aim of the note is to give a complete description of all the hyperplane sections 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 the homogeneous space $$\text {SL}_3({\mathbb {C}})/B$$ of the co-dimension one sub-scheme which is the union of two fundamental Schubert divisors.