Polynomial curves on trinomial hypersurfaces
Algebraic Geometry
2018-10-23 v1
Abstract
We prove that every rational trinomial affine hypersurface admits a horizontal polynomial curve. This result provides an explicit non-trivial polynomial solution to a trinomial equation. Also we show that a trinomial affine hypersurface admits a Schwartz-Halphen curve if and only if the trinomial comes from a platonic triple. It is a generalization of Schwartz-Halphen's Theorem for Pham-Brieskorn surfaces.
Cite
@article{arxiv.1706.05502,
title = {Polynomial curves on trinomial hypersurfaces},
author = {Ivan Arzhantsev},
journal= {arXiv preprint arXiv:1706.05502},
year = {2018}
}
Comments
11 pages