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arXiv · 0802.0705

Gonality, apolarity and hypercubics

Pietro De Poi·Francesco Zucconi
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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 $4/3g - 3$.

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Pietro De Poi, Francesco Zucconi. 2011-04-29. Gonality, apolarity and hypercubics. https://doi.org/10.1112/blms%2Fbdr021

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