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We compute Seshadri constantson  K 3 surfaces  X  of degrees 6 and 8. We also prove that if  X  is any embedded  K 3 surface of degree 2 r −2≥8 innot containing lines, then 1&lt; ε ( X )&lt;2 if and only if the homogeneous ideal of  X  is not generated by only quadrics (in which case).

Seshadri Constants of K 3 Surfaces of Degrees 6 and 8