

Iskovskikh Seminar
April 27, 2017 18:00, Moscow, Steklov Mathematical Institute, room 540






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.
Ivan Krasnov^{}, Arman Sarikyan^{} 
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Abstract:
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 3dimensional 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 $d1$ 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.

