A note on Seshadri constants on general $K3$ surfaces

Abstract

We prove a lower bound on the Seshadri constant $\epsilon (L)$ on a $K3$ surface $S$ with $\Pic S \simeq \ZZ[L]$. In particular, we obtain that $\epsilon (L)=\alpha$ if $L^2={\alpha }^2$ for an integer $\alpha$.

3 pages

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