Seshadri Constants of K3 Surfaces of Degrees 6 and 8

We compute Seshadri constants $\varepsilon(X):=\varepsilon(\mathcal O_X(1))$ on K3 surfaces X of degrees 6 and 8. We also prove that if X is any embedded K3 surface of degree 2r−2≥8 in $\mathbb P^r$ not containing lines, then 1<ε(X)<2 if and only if the homogeneous ideal of X is not generated by only quadrics (in which case $\varepsilon(X)=\frac {3}{2}$).