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arXiv · 0908.0522

Fermat hypersurfaces and Subcanonical curves

Pietro De Poi·Francesco Zucconi
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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. 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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Pietro De Poi, Francesco Zucconi. 2011-04-29. Fermat hypersurfaces and Subcanonical curves. https://doi.org/10.1142/s0129167x11007410

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