

Iskovskikh Seminar
November 27, 2014 18:00, Moscow, Steklov Mathematical Institute, room 540






Real forms of rational surfaces
E. A. Yasinsky^{} ^{} M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
A real form of complex quasiprojective variety $X$ is a real variety $X_0$
which complexification (as a scheme over $\mathbb{R}$) is isomorphic to $X$.
So one can ask a natural question: given some complex variety, how to
describe its real forms? In this short talk (based on the recent result of
Mohamed Benzerga) we show that if a rational surface $X$ has an infinite
number of nonequivalent real structures, then $X$ is a blowing up of
projective plane at $r \geq 10$ points. Surprisingly, this result is
connected with the question about solvability of the group of automorphisms
of $X$ acting trivially on Picard lattice.

