It is well known that total space of the tautological line bundle $\mathcal{O}(-1)$ over projective space $\mathbb{P}^n$ is closed subvariety of $\mathbb{P}^n\times\mathbb{A}^{n+1}$. My question is how to realize total space of $\mathcal{O}(1)$ over $\mathbb{P}^n$ in such manner, i.e. I need an embedding of $Tot(\mathcal{O}(1))$ in simple variety and defining equations. 
Thanks.



Total space of the line bundle $\mathcal{O}(1)$ over $\mathbb{P}^n$ 
It is the complement $\mathbb{P}^{n+1} - \{x\}$ of a point in a projective space. 


