Lucy Moser-Jauslin

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.

Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space

The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences of this structure and generalize some results to other hypersurfaces which arise as deformations of Koras–Russell threefolds.