6533b826fe1ef96bd12847ad
RESEARCH PRODUCT
Noncancellation for contractible affine threefolds
Pierre-marie PoloniLucy Moser-jauslinAdrien Duboulozsubject
Pure mathematicsApplied MathematicsGeneral Mathematics010102 general mathematics0103 physical sciences010307 mathematical physicsAffine transformation0101 mathematics01 natural sciencesContractible spaceMathematicsdescription
We construct two nonisomorphic contractible affine threefolds X X and Y Y with the property that their cylinders X × A 1 X\times \mathbb {A}^{1} and Y × A 1 Y\times \mathbb {A}^{1} are isomorphic, showing that the generalized Cancellation Problem has a negative answer in general for contractible affine threefolds. We also establish that X X and Y Y are actually biholomorphic as complex analytic varieties, providing the first example of a pair of biholomorphic but not isomorphic exotic A 3 \mathbb {A}^{3} ’s.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-05-02 | Proc. Amer. Math. Soc. |