曹锡华代数论坛

报告人： Ivan Cheltsov 教授 University of Edinburgh

中文题目： 关于 Cremona 群我们所知道的和不知道的

英文题目： What we know and what we do not know about Cremona groups?

时间： 2011年 3月 10 日 （周四） 下午 15：00-16：00

地点： 数学系126 教室





摘要

Cremona group of rank n is the group of birational automorphisms of n-dimensional projective space. The first results about the Cremona group of rank 2 go back to Apollonius of Perga (225-190 BC) who introduced the circle inversion, which is a birational involution of the real projective plane. Now we know a lot about the Cremona group of rank 2. We know its generators (Noether) and relations between them (Gizatulin). We know almost all its finite subgroups (Dolgachev and Iskovskikh), their conjugacy classes, dynamics of elements of infinite order etc. But many questions about the Cremona group of rank 2 are still open. Cremona groups of higher ranks are mistery to us. I will describe what we know about the Cremona group of rank 2, what we know about the Cremona group of rank 3 (recent results), and what we would like to know about them.