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arXiv · 1205.2982

Seshadri constants of $K3$ surfaces of degrees 6 and 8

Concettina Galati·Andreas Leopold Knutsen
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Abstract

We compute Seshadri constants $\eps(X):= \eps(Ø_X(1))$ on $K3$ surfaces $X$ of degrees 6 and 8. Moreover, more generally, we prove that if $X$ is any embedded $K3$ surface of degree $2r-2 \geq 8$ in $\PP^r$ not containing lines, then $1 < \eps(X) <2$ if and only if the homogeneous ideal of $X$ is not generated by only quadrics (in which case $\eps(X)=3/2$).

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Concettina Galati, Andreas Leopold Knutsen. 2012-09-04. Seshadri constants of $K3$ surfaces of degrees 6 and 8. https://doi.org/10.1093/imrn%2Frns174

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