Algebraic Geometry Seminar

---

Linearization problem for finite subgroups of the plane Cremona group

Speaker: Antoine Pinardin, The University of Edinburgh

Location: Warren Weaver Hall 512

Date: Tuesday, January 28, 2025, 5 p.m.

Synopsis:

The plane Cremona group is the group of birational self-maps of the projective plane. Over the field of complex numbers, its subgroups have been extensively studied, and the most complete classification dates back to 2006, with the work of Jérémy Blanc for abelian groups, and Dolgachev-Iskovskikh in the general case.

Although their classification up to isomorphism is essentially achieved, there is still a lot to be done if we consider the conjugacy classes of these subgroups. The latter authors point out a list of questions yet to be answered, in the final section, called "What is left?", of their paper. The first and main open problem they outline consists in finding all the so called linearizable subgroups of the plane Cremona group, namely those which are conjugated to a subgroup of linear automorphisms of the projective plane. It  remained open until now, and we give a complete answer to the problem.

This is a joint work with Arman Sarikyan and Egor Yasinsky.