On the compactifications of contractible affine threefolds and the Zariski cancellation problem (Q1762689)

The paper under review studies smooth contractible affine threefolds satisfying ``special'' embeddings in smooth projective threefolds. The speciality is a requirement on the numerical class of the boundary and on its Kodaira dimension. The author classifies all these threefolds. As a consequence the Zariski cancellation problem [see \textit{M. Zaidenberg}, in: Geometric complex analysis, Proc. conf. Hayama 1995, 691--714 (1996; Zbl 0934.14042)], is proved for this class of threefolds. The proof uses MMP techniques and the speciality condition is crucial to understand the modification occurring along the minimal model program. Then a very careful case by case analysis of all possible Mori spaces gives the classification.