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 $2r-2\ge 8$ 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 $\eps(X)=3/2$).

10 pages, 1 figure; to appear in IMRN with a more detailed bibliography

References in corpus (5)

• Seshadri constants on algebraic surfaces
• Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano Threefolds
• K3 projective models in scrolls
• Rational Curves on K3 Surfaces
• On the existence of curves with a triple point on a K3 surface

Cited by in corpus (3)

• On the degree of irrationality of low genus $K3$ surfaces
• A note on Seshadri constants of line bundles on hyperelliptic surfaces
• Local numerical equivalences and Okounkov bodies in higher dimensions