A note on geometric facoriality. (English) Zbl 0851.13007
Author’s abstract: Let \(k\) be a perfect field such that \(\overline {k}\) is solvable over \(k\). We show that a smooth, affine, factorial surface birationally dominated by affine 2-space \(\mathbb{A}^2_k\) is geometrically factorial and hence isomorphic to \(\mathbb{A}^2_k\). The result is useful in the study of subalgebras of polynomial algebras. The condition of solvability would be unnecessary if a question we pose on integral representations of finite groups has a positive answer.
Reviewer: E.Stagnaro (Padova)
MSC:
13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |
20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
14A05 | Relevant commutative algebra |