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Jordan property for automorphism groups of projective varieties

Prof.
De-Qi Zhang
Institution: 
National University of Singapore
Location: 
Lecture Room 5A (Sezione di Matematica e Informatica, H2 building, Via Valerio 12/1, 5th floor)
Schedule: 
Wednesday, December 11, 2019 - 14:00
Abstract: 

A century ago, Camille Jordan proved that the complex general linear group $GL_n(C)$ has the Jordan property: there is a Jordan constant $C_n$ such that every finite subgroup $H < GL_n(C)$ has an abelian subgroup $H1$ of index $[H:H1] < C_n$. 
We show that every connected algebraic group $G$ (which is not necessarily linear) has the Jordan property with the Jordan constant depending only on $dim G$, and that the full automorphism group $Aut(X)$ of every projective variety $X$ has the Jordan property.
We will also mention recent results on the Jordan property of birational groups of algebraic varieties and automorphism groups of complex manifolds.

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