Affine surfaces with isomorphic $\mathbb{A}^2$-cylinders

Adrien Dubouloz (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We show that all complements of cuspidal hyperplane sections of smooth projective cubic surfaces have isomorphic A(2)-cylinders. As a consequence, we derive that the A(2)-cancellation problem fails in every dimension greater than or equal to 2.

Mots clés: varieties; cancellation problem

Domaines: Mathématiques [math]

Adrien Dubouloz. Affine surfaces with isomorphic $\mathbb{A}^2$-cylinders. Kyoto Journal of Mathematics, 2019, 59 (1), pp.181-193. ⟨10.1215/21562261-2018-0005⟩. ⟨hal-02166793⟩