On the irreducibility of Severi varieties on 𝐾3 surfaces

Abstract

Let ( S , L ) (S,L) be a polarized K 3 K3 surface of genus p ⩾ 11 p \geqslant 11 such that Pic ( S ) = Z [ L ] \textrm {Pic}(S)=\mathbf {Z}[L] and δ \delta is a non-negative integer. We prove that if p ⩾ 4 δ − 3 p\geqslant 4\delta -3 , then the Severi variety of δ \delta -nodal curves in | L | |L| is irreducible.