The biregular cancellation problem (Q1100237)

The biregular cancellation problem asks if two affine varieties \(V_ 1\), \(V_ 2\) are biregularly isomorphic, shortly \(V_ 1\cong V_ 2\), when \(V_ 1\times {\mathbb{A}}^ n\cong V_ 2\times {\mathbb{A}}^ n\). If \(V_ 2\times {\mathbb{A}}^ n\cong A^{n+2}\) then \(V_ 1\cong {\mathbb{A}}^ 2\) as shows the results of Fujita, Miyanishi and Sugie. Here there are some results on the biregular cancellation problem of nonrational surfaces.