Date:
Thu, 12/01/202313:00-14:00
Location:
Levy 6 Hall and Zoom
Zoom Link: https://huji.zoom.us/j/84511564169?pwd=SkJmY285YnFIWkZqNmxuaVZsVVQ2UT09
Meeting ID: 845 1156 4169
Passcode: 171220
Title: Rigid birational involutions of \PP^3.
Abstract:
The Cremona group Cr_n(\kk) is the group of birational transformations of \PP^n over a field \kk.
The study of these groups dates back to the 19th century with some of the central questions still remaining open.
In the recent years new techniques, based on the Minimal Model Program, have been developed to answer some of these questions when \kk = \CC.
In this talk, after briefly introducing the main machinery, I will construct families of birational involutions of \PP^3 and use them to obtain a free product structure on Cr_3(\CC).
As a direct corollary we obtain a new and effective proof of the non-simplicity of Cr_3(\CC).
If time permits, I will show how to use the free product structure to prove that the group \Aut(Cr_3(\CC)) is not generated by inner and field automorphisms.
Meeting ID: 845 1156 4169
Passcode: 171220
Title: Rigid birational involutions of \PP^3.
Abstract:
The Cremona group Cr_n(\kk) is the group of birational transformations of \PP^n over a field \kk.
The study of these groups dates back to the 19th century with some of the central questions still remaining open.
In the recent years new techniques, based on the Minimal Model Program, have been developed to answer some of these questions when \kk = \CC.
In this talk, after briefly introducing the main machinery, I will construct families of birational involutions of \PP^3 and use them to obtain a free product structure on Cr_3(\CC).
As a direct corollary we obtain a new and effective proof of the non-simplicity of Cr_3(\CC).
If time permits, I will show how to use the free product structure to prove that the group \Aut(Cr_3(\CC)) is not generated by inner and field automorphisms.