Invariant Hilbert schemes and invariant deformation theory
Ronan Terpereau (Mainz)
What 


When 
Dec 05, 2013 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
Add event to calendar 
vCal iCal 
Abstract. Let $G$ be an algebraic
group acting on a vector space $W$. In this talk we are interested by the
invariant Hilbert scheme $H=Hilb^G(W)$, which is the moduli space of the
$G$stable closed subschemes $X \subset W$ whose affine algebra $\mathbb{C}[X]$
is the direct sum of simple $G$modules with previously fixed finite
multiplicities. Many examples of such $H$ have been determined during the last
fifteen years, most of them for $G$ a finite group or a torus. If $G$ is
arbitrary and $H$ is singular, then it is generally very difficult to determine
whether $H$ is reducible, reduced...
On the other hand, the deformation theory is an old and wellknown field of the
algebraic geometry, but the $G$invariant version is quite recent and once
again very few is know when $G$ is arbitrary.
The aim of this talk is to show the relation between these two topics, and to
explain how the invariant deformation theory can be used to determine new
examples of invariant Hilbert schemes. As an application, we will discuss some explicit
examples where $G \subset GL_3$ is a classical group acting on a classical
representation.