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Abstract: In the talk we will consider del Pezzo surfaces of degree 8 over algebraically nonclosed fields of characteristic 0. Any quadric surface in three-dimensional projective space is a del Pezzo surface of degree 8, and it is well known that such surface can be pointless. We want to study birational classification of quotients of pointless del Pezzo surfaces of degree 8 by finite automorphism groups. In particular, we want to find conditions on the surface and the group for which the quotient can be not rational over the main field. We will show that the quotient by any group of odd order is birationally equivalent to the original surface, and the quotient by any group of even order is birationally equivalent to a quadric surface.
Bio: Andrey Trepalin graduated from the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University in 2010 and obtained his PhD at Institute for Information Transmission Problems in 2014 in Moscow. Then he was a scientific researcher in Institute for Information Transmission Problems. Now he is a scientific researcher in the Department of Algebra of Steklov Mathematical Institute of RAS and in the Laboratory of Algebraic Geometry of Higher School of Economics in Moscow. His research interests are in algebraic geometry, especially birational geometry.
