Workshop on birational geometry
November 19, 2020
 
Abstracts of the talks
 

Artem Avilov (HSE)
G-birationally rigid del Pezzo threefolds
In this talk we will consider rational del Pezzo threefolds of degree 2. We will classify the ones which are G-birationally rigid for some finite group. In particular we will find several embeddings of S4 into the space Cremona group.


Olivier Haution (LMU)
The cobordism ring of algebraic involutions
I will provide an elementary definition of the cobordism ring of involutions of smooth projective varieties over a field (of characteristic not 2). I will describe its structure, and give explicit "stable" polynomial generators. I will draw some concrete consequences concerning the geometry of fixed loci of involutions, in terms of Chern numbers. I will in particular mention an algebraic version of Boardman's five halves theorem.


Hsueh-Yung Lin (IPMU)
Algebraic approximations of compact Kähler threefolds
Let X be a compact Kähler manifold. The so-called Kodaira problem asks whether X has arbitrarily small deformations to some projective varieties. We will provide an overview of the proof showing that such deformations always exist for compact Kähler threefolds.


Sheng Meng (KIAS)
Jordan property for varieties
A group is Jordan if all its finite subgroups are "almost" abelian (up to a bounded index). Such property is related to several boundedness problems.
In this talk, I'll survey several known results and technique on automorphism groups of varieties.



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