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In this note we study the image of $\PP^2$ in $\text{Gr}(2, \CC^{4})$ givenby tangent bundle of $\PP^2. $ We show that there is component $\mathcal{H}$ ofthe Hibert scheme of surfaces in $\text{Gr}(2, \CC^{4})$ with no point of itcorresponds to a smooth surface.

Tangent bundle of $\PP^2$ and morphism from $\PP^2$ to $\text{Gr}(2, \CC^{4})$