Finite-projection stabilization of contractible affine hypersurfaces

Scope of the work

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.

Reproduction notes

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Author disclosures

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References and related publications

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