Speaker
Tommaso de Fernex (University of Utah-USA)
Title
Local geometry of spaces of
arcs
Abstract
The arc space
of a variety is an infinite
dimensional scheme whose geometric structure captures, in a way that is not
yet fully understood, certain features of
the singularities of the variety.
Focusing on its local rings and invariants of these rings such as embedding dimension
and codimension, we explore the local structure of arc spaces. Our main
tools rely on a formula for the sheaf
of differentials on arc spaces and some recent finiteness results on the fibers of the map induced at the level of arc spaces
from an arbitrary morphism
of schemes over a field. The talk is
based on joint work with Christopher Chiu and Roi Docampo.