Seshadri constants of K3 surfaces of degrees 6 and 8
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≥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 $\eps(X)=3/2$).