The exposition reports projective versions of K3 surfaces whose hyperplane sections are non-Clifford common curves. those versions are contained in rational basic scrolls. The exposition vitamins normal descriptions of types of common K3 surfaces in projective areas of low size, and results in a class of K3 surfaces in projective areas of size at such a lot 10. The authors convey extra the guidelines in Saint-Donat's classical article from 1974, lifting effects from canonical curves to K3 surfaces and incorporating a lot of the Brill-Noether thought of curves and idea of syzygies built in the meanwhile.
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