Cancellation for Surfaces Revisited

The celebrated Zariski Cancellation Problem asks as to when the existence of an isomorphism X × A n ≅ encoding="application/x-tex">X_\lambda \to \times We construct versal deformation families their coarse moduli spaces provided nonconstant invertible functions. Each these has infinite number irreducible components growing dimensions; each component variety singularities. Finally, analyze from our viewpoint examples non-cancellation constructed Danielewski, tom Dieck, Wilkens, Masuda Miyanishi, e.a.