On the irreducibility of Severi varieties on K3 surfaces

Ciro Ciliberto, Thomas Dedieu

Let $(S,L)$ be a polarized $K3$ surface of genus $p⩾11$ such that $\mathrm{Pic}(S)=\mathbf{Z}[L]$, and $\delta$ a non-negative integer. We prove that if $p⩾4\delta -3$, the…