Fermat hypersurfaces and Subcanonical curves

Details Fermat hypersurfaces and Subcanonical curves Fermat hypersurfaces and Subcanonical curves

2009-08-04

arxiv.org/abs/0908.0522v4

Mathematics

Algebraic Geometry

18 pages; AMS-LaTeX

Scientific paper

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. Moreover, we show that
any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical
$(s+2)$-gonal projectively normal curve, and vice versa.

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