Fermat hypersurfaces and Subcanonical curves

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.

18 pages; AMS-LaTeX

References in corpus (1)

• Gonality, apolarity and hypercubics

Cited by in corpus (1)

• On the cactus rank of cubics forms