Meaning of a the notation $P(E)$, where $E$ is a sheaf.

Question

I am reading a paper where I find this sentence :

"Let $Y=\mathbb P^1$ and $E$ a locally free sheaf on $Y$ of rank $r$. We put $X=\mathbb P(E)$, and let us denote by $\pi:X\rightarrow Y$ the canonical map, so $\pi_*(\mathcal O_X(1))\simeq E$."

My question is : What is $\mathbb P(E)$?

Thank you.

Answer 1

$\mathbb{P}(E) = \mathrm{Proj}\left( \bigoplus_{k=0}^\infty \mathrm{Sym}^kE \right)$.