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arXiv · 1706.05502

Polynomial curves on trinomial hypersurfaces

Ivan Arzhantsev
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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.

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Ivan Arzhantsev. 2017-06-17. Polynomial curves on trinomial hypersurfaces. https://doi.org/10.4064/aa170813-18-2

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