Pierre-Marie Poloni

Noncancellation for contractible affine threefolds

We construct two nonisomorphic contractible affine threefolds X and Y with the property that their cylinders X×A1 and Y ×A1 are isomorphic, showing that the generalized Cancellation Problem has a negative answer in general for contractible affine threefolds. We also establish that X and Y are actually biholomorphic as complex analytic varieties, providing the first example of a pair of biholomorphic but not isomorphic exotic A3’s.

Affine-ruled varieties without the Laurent cancellation property

We describe a method to construct hypersurfaces of the complex affine

Extension of Automorphisms of Rational Smooth Affine Curves

n

Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space

-space with isomorphic

On a class of Danielewski surfaces in affine 3-space

\mathbb{C}^*

Inequivalent embeddings of the Koras-Russell cubic 3-fold

-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e. hypersurfaces that are non isomorphic, although their

Embeddings of a family of Danielewski hypersurfaces and certain C⁺-actions on C³

\mathbb{C}^*

Classification(s) of Danielewski hypersurfaces

-cylinders are isomorphic as abstract algebraic varieties. We also provide examples of non isomorphic varieties

Noncancellation for smooth contractible affine threefolds

X

The density property for Gizatullin surfaces completed by four rational curves

and