Conférence GAGC 2016 (en 2017)

Enumeration of curves on K3 surfaces by polyhedral degenerations

Non programmé

50m

CIRM, Luminy

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.