Gonality, apolarity and hypercubics

Details Gonality, apolarity and hypercubics Gonality, apolarity and hypercubics

2008-02-05

arxiv.org/abs/0802.0705v4

Mathematics

Algebraic Geometry

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

Scientific paper

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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