The holomorphic cancellation problem asks whether a complex manifold 
with 
biholomorphic to 
must be biholomorphic to 
. Biholomorphic means that the map and its inverse
are holomorphic. The holomorphic problem
is distinct from the algebraic Zariski
cancellation problem, which requires algebraic isomorphisms
(Huang 2026).
Assuming an announced exotic-affine-space result of Auroux, Bai, and Pomerleano, Huang (2026) constructed a counterexample for some integer 
with 
. In that example, a complex affine
variety 
is not biholomorphic to 
but 
is biholomorphic to 
.
