I wanted to show the following proposition:
Let $n,d \in \mathbb{N}^{\ast}$ and let us denote $V= \mathbb{K}[x_0, \dots , x_n]_d$ the vector space of homogeneous polymials. Let us consider the Universal Hypersurface $$H:= \{ ([x],F) \in \mathbb{P}^n \times V \, | \, F(x) = 0 \}$$ Then H is a quasi-projective variety.
Actually I got stuck since I know very few things about projective varieties (only basics). I would really appreciate any hint to figure out how to prove the quasi-projectivity.
Thanks you in advance.
K. Y.