On the irreducibility of Severi varieties on K3 surfaces

Ciro Ciliberto; Thomas Dedieu

On the irreducibility of Severi varieties on K3 surfaces

Algebraic Geometry 2019-06-28 v3

Authors: Ciro Ciliberto , Thomas Dedieu

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.

Keywords

severi varieties k3 surfaces irreducibility polarized surfaces nodal curves

Cite

@article{arxiv.1809.03914,
  title  = {On the irreducibility of Severi varieties on K3 surfaces},
  author = {Ciro Ciliberto and Thomas Dedieu},
  journal= {arXiv preprint arXiv:1809.03914},
  year   = {2019}
}

Comments

Minor correction in 4.2.2.b. Final version, to appear in Proceedings of the AMS

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