Severi Varieties of nodal curves on surfaces

Date(s) : 07/02/2017   iCal
11 h 00 min - 12 h 00 min

Given any algebraic projective curve $C$, it can be realized as a plane curve with at most nodes. For this reason, starting with F. Enriques and F. Severi in the first couple of decades of last century, algebraic geometers started getting interested in families of plane curves with a fixed degree $d$ and a given number $\delta$ of nodes. In more recent times these families have been baptized \emph{Severi varieties} and suitable versions of them have been considered also on surfaces other than the projective plane, especially on $K3$ surfaces The study of Severi varieties, in the plane as well as in other surfaces, is a milestone in algebraic geometry, has several interesting and attractive aspects and is quite active nowadays, especially concerning enumerative questions. In this talk I will try to summarize some of the main known results on the subject and explain a variety of different techniques introduced for studying them. Time permitting, I will in particular mention some work in progress with Th. Dedieu on the subject, based on degeneration techniques.


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