= K3 linear system dichotomies
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= K3 dichotomies
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{synonym}
For nef big systems on a complex <K3 surface>, the successive alternatives distinguish a <monogonal linear system on a K3 surface> from a basepoint-free system; then a degree-two map from a birational map; then a projective ideal generated by quadrics from the trigonal and plane-quintic exceptions. The last alternatives must include the low-genus quartic and quadric-cubic models. The birational morphism can contract exactly the orthogonal $(-2)$-curves; it need not embed the original smooth surface.
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