On the constructions relating moduli of Del Pezzo surfaces, plane curves and configurations of points.

A Del Pezzo surface of degree $d$ is a smooth complex proper surface $X$ so that the anticanonical divisor $-K_X$ is ample and satisfies $K^2_X = d$. Del Pezzo surfaces are obtained by the blow up of $\mathbb{P}^2$ at certain number points. Our aim is to find a one and one correspondance between the moduli spaces of Del Pezzo surfaces of degree $2$ and the moduli spaces of configurations points in $\mathbb{P}^2$ and exdend the result to a general case of Moduli Spaces of Del Pezzo surfaces of degree $d \ge 2$.