A Nodal Decic Counterexample to the Generic Projection Incidence Bound
Year: 2026
Type: preprint
Abstract: We construct a degree-ten hypersurface in complex projective four-space with exactly sixty ordinary double points whose general plane projection lies on a sextic. Thus the projected nodes violate the proposed bound k(n-1), since 60 > 6(10-1) = 54, even though 60 < (10-1)^2. This answers negatively the projection question in Cheltsov's Problem 18 in an AIM workshop list and gives a counterexample to Cheltsov-Park Conjecture 1.6. The node set satisfies the stronger ambient incidence bound 7k for curves of degree k. We use the known sextic-projection property of the projectivized H4 roots, realize those points as nodes of an explicit symmetric decic surface, and remove every unwanted singularity after extending to a threefold. Exact Hessian, Groebner-basis and interpolation certificates accompany the construction. The threefold is factorial; the separate sharp factoriality theorem is not contradicted. This is an AI-assisted, self-audited, unrefereed preprint; it makes no independent-review, formal-certification or absolute-priority claim.
Author: Ferudun, Alper
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222905329
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