The exposition reports projective versions of K3 surfaces whose hyperplane sections are non-Clifford common curves. those types are contained in rational general scrolls. The exposition vitamins average descriptions of versions of common K3 surfaces in projective areas of low measurement, and results in a category of K3 surfaces in projective areas of measurement at such a lot 10. The authors carry 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 concept of syzygies constructed at the moment.

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