Orateur
Thomas Dedieu
Description
Let $(S,L)$ be a primitively polarized K3 surface, $k$ an
integer. Integral curves of geometric genus $g$ in the linear
system $|kL|$ form a family of dimension $g$ (if non-empty).
One wants to count the number of such curves passing through
$g$ general points fixed on $S$.
Gromov-Witten theory provides a complete answer to this
question when $k=1$, but poses serious problems when$ k>1$. I
shall present an approach based upon degenerating the
surface $S$ immersed by the system $|kL|$ in a union of planes
incarnating a triangulation of the $S^2$ sphere.
This is a joint project with Ciro Ciliberto.
