I. Krasnov. Rational singular del Pezzo surfaces with the Picard group isomorphic $\mathbb{Z}$. “Visual” proof of the theorem on the classification of such surfaces. A. Sarikyan. On the Picard group of cubic surface

I. Krasnov.
I will consider the rational singular del Pezzo surfaces with the Picard group isomorphic to $\mathbb{Z}$. In addition, I will try to give an alternative, “visual” proof of the theorem of the classification of such surfaces, given in M. Furushima's article "Singular del Pezzo surfaces and analytic compactifications of 3-dimensional complex affine space $\mathbb{C}^3$", Nagoya Math J. Vol. 104 (1986). I will tell about how to get a del Pezzo surface of degree $d-1$ from a surface degree $d$. In addition, I will try to write down the equations of singular surfaces of degree 3, 2, and 1.
A. Sarikyan.
I will talk about the Picard group of a cubic surface $a_0x_0^3 + a_1x_1^3 + a_2x_2^3 + a_3x_3^3$. I will show when such a surface is unirational but not rational, and I will describe the action of the Galois group on the Picard group of this surface.