We compute Seshadri constants $\eps(X):= \eps(\O_X(1))$ on $K3$ surfaces $X$ of degrees $6$ and $8$. 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 $\eps(X)=\frac{3}{2}$).
Seshadri constants of $K3$ surfaces of degrees $6$ and $8$ / Galati, Concettina; Knutsen, A. L.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 17(2013), pp. 4072-4084.
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Titolo: | Seshadri constants of $K3$ surfaces of degrees $6$ and $8$ |
Autori: | |
Data di pubblicazione: | 2013 |
Rivista: | |
Citazione: | Seshadri constants of $K3$ surfaces of degrees $6$ and $8$ / Galati, Concettina; Knutsen, A. L.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 17(2013), pp. 4072-4084. |
Handle: | http://hdl.handle.net/20.500.11770/137082 |
Appare nelle tipologie: | 1.1 Articolo in rivista |