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 
. The dependency on the announced result is part of the
claim and is not independently verified here. Huang (2026) reports generative AI
assistance in developing the proofs and assumes responsibility
for their content.
