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  1. Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theoremScott SchubrEdition 3 · 2026-10-27 Public
  2. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  3. Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificatesScott SchubrEdition 3 · 2026-10-27 Public
  4. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
  5. Fekete convergence from balanced integer predecessors in shrinking corridorsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp trace-degree certificates for rank-two permanent-derivative compensationScott SchubrEdition 2 · 2026-10-27 Public
  7. Residual Certificates and Empirical Sharpness for Entropic Self-Transport ScoresScott SchubrEdition 2 · 2026-10-27 Public
  8. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  9. Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-TransportScott SchubrEdition 2 · 2026-10-27 Public
  10. Finite-spectral recovery of Weyl-blind twisting modesScott SchubrEdition 2 · 2026-10-27 Public
  11. Local comparison counting for linear extensions and a bounded-range balance refinementScott SchubrEdition 2 · 2026-10-27 Public
  12. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  13. A quantitative Chollet inequality for rank-four matrices of order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Single-copy learning of stabilizers with correlated diagonal noiseScott SchubrEdition 2 · 2026-10-27 Public
  15. Relative finite optimization of arithmetic approximation distancesScott SchubrEdition 2 · 2026-10-27 Public
  16. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  17. Frequency Localization for Weil Operator CertificatesScott SchubrEdition 3 · 2026-10-27 Public
  18. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  19. Joint Cutoffs and Negative-Spectrum Decay for Weighted Weil OperatorsScott SchubrEdition 3 · 2026-10-27 Public
  20. Sharp convergence of heat-kernel Sinkhorn metricsScott SchubrEdition 2 · 2026-10-27 Public
  21. Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentrationScott SchubrEdition 2 · 2026-10-27 Public
  22. Curvature classification and certified Sinkhorn metrics for Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  23. Mean ergodic convergence from near-diagonal subadditivityScott SchubrEdition 2 · 2026-10-27 Public
  24. Quantitative Null-Space Compression for a Weighted Weil OperatorScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 4

Finite-projection holomorphic stabilization of contractible affine manifolds

Scott Schubr

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Abstract

Let X be a smooth contractible affine manifold of dimension n≥2 with the holomorphic density property. We prove that X × ℂⁿ ≅ ℂ²ⁿ holomorphically whenever X admits a finite flat morphism to ℂⁿ with curvilinear scheme fibers. A global algebra generator is unnecessary: local primitive elements describe the fiber embedding spaces, and stratified Oka section existence supplies a fiberwise embedding into a Runge Euclidean basin. Entire interpolation and parametric Andersén–Lempert approximation then give compact capture and a Runge-ball exhaustion. Every smooth affine surface or threefold admits a finite flat linear projection with curvilinear fibers, so the stabilization conclusion holds for all contractible density-property examples in these dimensions. It also holds for affine hypersurfaces in every dimension n≥2, saving one stabilizing direction relative to Huang's proper-embedding construction. The applications include McLean's varieties, the Koras–Russell cubic, and sufficient dimension reductions in specified nonlinearizable-action constructions, with disconnected cyclic fixed loci on ℂ⁶ and a contractible non-Euclidean fixed surface on ℂ⁸.

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