Polynomial curves on trinomial hypersurfaces

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.

11 pages

References in corpus (3)

• Log terminal singularities, platonic tuples and iteration of Cox rings
• Non-complete rational T-varieties of complexity one
• On iteration of Cox rings

Cited by in corpus (1)

• Generalization of the ABC theorem on locally nilpotent derivations