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Meeting ID: 891 3880 1618
Abstract: A conic bundle is a flat morphism $f: X\to Z$ of smooth algebraic varieties whose fibers are plane conics. I will discuss the problem of rationality of algebraic varieties having conic bundle structures. First, I recall almost classical results on birational properties of surface conic bundles over non-closed fields. Then I concentrate on the three-dimensional case. The main focus will be on the conjectural criterion of rationality.
Bio: Yuri Prokhorov is a Chief Scientific Researcher of the Department of Algebraic Geometry of the Steklov Mathematical Institute of the Russian Academy of Sciences and a Professor at the Lomonosov Moscow State University. He is a Corresponding Member of the Russian Academy of Sciences. He was an invited speaker at the 8th European Congress of Mathematics in 2021. He was an invited speaker at the International Congress of Mathematicians 2022 in the section Algebraic and Complex Geometry. His research interests are in algebraic geometry (especially birational geometry).