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arXiv · 1809.03914

On the irreducibility of Severi varieties on K3 surfaces

Ciro Ciliberto·Thomas Dedieu
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Abstract

Let $(S,L)$ be a polarized $K3$ surface of genus $p \geqslant 11$ such that $\mathrm{Pic}(S)=\mathbf{Z}[L]$, and $\delta$ 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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Ciro Ciliberto, Thomas Dedieu. 2018-09-11. On the irreducibility of Severi varieties on K3 surfaces. https://arxiv.org/abs/1809.03914

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