Seminar in Real and Complex Geometry
Wednesday, 13.05.2015, 16:00-17:00,
building, room 210
Steklov Mathematical Institute
Plane rational quartics and $K3$ surfaces
The talk is devoted to the actions of the symmetric group $\mathbb S_4$ on $K3$ surfaces $X$
satisfying the following properties:
\item[$(*)$] the action of the alternating group $\mathbb A_4\subset \mathbb S_4$ on $X$ is
\item[$(**)$] there is an equivariant birational contraction $r: X\to \overline X$ to a surface
$\overline X$ with $A-D-E$-singularities such that
$\overline X/\mathbb S_4\simeq \mathbb P^2$.
It will be explained that up to smooth equivariant deformations there are exactly 16 such
of $\mathbb S_4$ on the $K3$ surfaces and all these actions are realised as the actions of the
on the Galois closures $\overline X$ of the dualising
coverings of the projective plane associated with plane rational quartics having no the
of the types $A_4$, $A_6$, and $E_6$.