Zariski cancellation and affine fibrations over the complex numbers
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
Affine-space cancellation asks whether $X\times\mathbb A^1\cong\mathbb A^{n+1}$ forces $X\cong\mathbb A^n$. The formalized result gives an explicit finite-type complex domain $A$ of Krull dimension four with $A[w]\cong\mathbb C[x_1,\ldots,x_5]$ but $A\not\cong\mathbb C[x_1,\ldots,x_4]$. Thus adjoining one variable erases a genuine algebraic distinction.
The separate stable-coordinate and general line-bundle lifting consequences are not included.
Comparator links
| Result | Comparator statement |
|---|---|
| Complex affine-space cancellation counterexample | ComplexCancellation.lean |