Affine threefolds with \(\mathbb{A}^{2}\)-fibrations. (English) Zbl 1439.14177
Summary: An affine threefold containing an \(\mathbb{A}^{2}\)-cylinder is studied. The existence of \(\mathbb{A}^{2}\)-cylinders is almost equivalent to the existence of mutually commuting, independent \(G_a\)-actions \(\sigma_{1}, \sigma_{2}\). A typical example of such affine threefolds is a hypersurface \(x^m y = f(x, z, t)\), and we generalize such a hypersurface to define an affine pseudo-3-space. After I. Hedén [“Russell’s hypersurface from a geometric point of view”, Preprint, arXiv:1405.4561], we observe also a \(G_a\)-action on the hypersurface \(x^{m}y = f(x, z, t)\) with \(m\geq 2\).
MSC:
| 14R05 | Classification of affine varieties |
| 14R10 | Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) |
| 14R25 | Affine fibrations |
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