We extend the classical Enriques–Petri theorem to s-subcanonical projectively normal curves, proving that such a curve is (s+2)-gonal if and only if it is contained in a surface of minimal degree. We also show that any Fermat hypersurface of degree s+2 is apolar to a s-subcanonical (s+2)-gonal projectively normal curve, and vice versa.
Fermat hypersurfaces and subcanonical curves
DE POI, Pietro;ZUCCONI, Francesco
2011-01-01
Abstract
We extend the classical Enriques–Petri theorem to s-subcanonical projectively normal curves, proving that such a curve is (s+2)-gonal if and only if it is contained in a surface of minimal degree. We also show that any Fermat hypersurface of degree s+2 is apolar to a s-subcanonical (s+2)-gonal projectively normal curve, and vice versa.File in questo prodotto:
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