Counting sums of two powers
Algebraic Geometry
2025-07-14 v1
Abstract
We generalize two well-known enumerative facts. The first, due to Clebsch, says that a general binary sextic form is expressible as the sum of a cube and a square in 40 different ways. The second, due to Zariski and later Vakil, states that a general pencil of binary 12-ics contains exactly 3762 cubes plus squares, ignoring scaling.
Keywords
Cite
@article{arxiv.2507.08337,
title = {Counting sums of two powers},
author = {Anand Patel},
journal= {arXiv preprint arXiv:2507.08337},
year = {2025}
}