Speaker: Prof. Konstantin Shramov， Steklov Mathematical Institute and NRU Higher School of Economics

Title: Del Pezzo surfaces of degree 4
Language: English
Time & Venue: 2024.04.17 10:00-11:30 MCM110

Abstract: A del Pezzo surface is a smooth projective surface with ample anticanonical divisor. Over an algebraically closed field, any surface like this is rational. However, without this assumption del Pezzo surfaces exhibit very interesting birational properties. I will survey some old and new results about birational geometry of del Pezzo surfaces over arbitrary fields, mostly focusing on del Pezzo surfaces of degree 4. These can be realized as intersections of two quadrics. It is known that minimal del Pezzo surfaces of degree 4 over a perfect field are never rational. I will provide a detailed description of birational models for such surfaces, and will discuss the properties of their birational automorphism groups. The talk is based on a joint work in progress with A.Trepalin.