On the irreducibility of Severi varieties on 𝐾3 surfaces

Ciliberto, C.; Dedieu, Th.

doi:10.1090/proc/14559

On the irreducibility of Severi varieties on $K3$ surfaces
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by C. Ciliberto and Th. Dedieu PDF

Proc. Amer. Math. Soc. 147 (2019), 4233-4244 Request permission

Abstract:

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

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