Finite-projection stabilization of contractible affine hypersurfaces

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1. Edition 4 · 2026-11-02 · public
2. Edition 3 · 2026-10-27 · public
3. Edition 2 · 2026-10-24 · public
4. Edition 1 · 2026-10-24 · public

Subjects

Mathematics · Complex Analysis · Geometry

Keywords

holomorphic cancellation, density property, Oka principle, affine hypersurfaces, finite schemes

Manuscript date

2026-10-23

Reader reuse

No additional permission granted

Scope

Let X be a smooth contractible affine hypersurface of complex dimension n >= 2 with the holomorphic density property. We prove that X times C^n is biholomorphic to C^(2n). A finite monic projection replaces the proper-embedding parameter in Huang’s stabilization construction, retaining colliding fibers as curvilinear finite schemes. Stratified Oka interpolation and parametric Andersén-Lempert approximation yield compact capture in a fixed Runge Euclidean basin. Applications include McLean’s varieties and the Koras-Russell cubic. The sufficient ambient dimensions in specified nonlinearizable-action constructions are lowered by one, including disconnected cyclic fixed loci in C^6 and a fixed contractible non-Euclidean surface in C^8.

Disclosures

AI-assisted tools supported research exploration, literature review, manuscript preparation and internal verification. The author retains responsibility for the work.

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The exact publication package includes the 9-page manuscript, editable LaTeX sources, reader/build instructions, citation metadata, public checksums and any necessary mathematical or computational supplements. Keep its 6 members together and follow the included README for dependencies, build commands and any finite verification programs. Published finite checks support the stated analytic arguments.

References and related resources

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