Iskovskikh Seminar April 11, 2024 18:00, Moscow, Steklov Mathematical Institute, room 530
The dual complex of a $G$-variety
A. Shipenok
Abstract:
Let $G$ be a finite group acting on a smooth projective variety.
An important problem is the classification of $G$-varieties up to $G$-birational
equivalence.
In the talk, a dual complex will be constructed, the highest homology group of
which is a $G$-birational invariant.
Using this invariant, new examples of varieties with the action of a group $G$
will be constructed, which cannot be $G$-equivariantly rearranged into a
projective space.
In particular, we demonstrate the non-linearizability of some actions of an
abelian group of high rank on smooth hypersurfaces in a projective space of
any dimension and degree at least 3.
The talk is based on the paper: Louis Esser, "The dual complex of a $G$-variety".