On smooth surfaces in projective four-space lying on quartic hypersurfaces with isolated singularities
classification
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four-spacegeneralisolatedprojectiveprovequarticsingularitiessmooth
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We prove that a smooth surface, non of general type, in projective four-space, which lies on a quartic hypersurface with isolated singularities has degree at most 27 (in fact we prove a slightly more general result).
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