Birational involutions of the projective plane

Egor Yasinsky (École Polytechnique)

24-Mar-2022, 11:00-12:00 (2 years ago)

Abstract: Birational involutions of the projective plane (or, equivalently, automorphisms of the field of rational functions in two variables of order 2) were studied already by the Italian school of algebraic geometry — Bertini, Castelnuovo, and Enriques. However, their explicit and complete description was obtained by Beauville and Bayle only in 2000 and only in the case of a complex projective plane. It turns out that for planes over algebraically non-closed fields the situation is much more complicated. In the first part of the talk, I will review what is known about birational involutions of projective planes over various fields. In the second part, I will talk about the joint work with I. Cheltsov, F. Mangolt and S. Zimmerman, in which we classified birational involutions of the real projective plane.

algebraic geometrycombinatorics

Audience: researchers in the topic


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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