Gonality, apolarity and hypercubics

Abstract

We show that any Fermat hypercubic is apolar to a trigonal curve, and vice versa. We show also that the Waring number of the polar hypercubic associated to a tetragonal curve of genus $g$ is at most $\lceil 3/2g-7/2\rceil$, and for a large class of them is at most $4/3g-3$.

9 pages, to appear in the Bulletin of the London Mathematical Society

References in corpus (2)

• Green-Lazarsfeld's Conjecture for Generic Curves of Large Gonality
• Families of n-gonal curves with maximal variation of moduli

Cited by in corpus (2)

• On the cactus rank of cubics forms
• Fermat hypersurfaces and Subcanonical curves