Deformations of singularities and variations of GIT quotients I -- Radu Laza


<p>In this talk we will discuss the deformations of two classes of  singularities: the
minimally elliptic surface singularity $N_{16}$  and the threefold singularity $O_{16}$
(the cone over a cubic  surface). Via a standard procedure, due to Pinkham, the study of
the  deformations of $N_{16}$ is reduced to the study of a moduli space of  pairs $(C,L)$
consisting of a plane quintic curve and a line. We  construct this moduli space of pairs
by using both Hodge theory and  GIT. Each construction provides complementary
information, and  together they offer a complete description of the deformations of $N_
{16}$. Similar considerations apply for $O_{16}$.