Document Zbl 1471.13056 - zbMATH Open
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Locally nilpotent derivations of double Danielewski surfaces. (English) Zbl 1471.13056
In the article under review, the authors consider a particular class of smooth affine surfaces over a field \(k\) of characteristic zero admitting algebraic actions of the additive group \(\mathbb{G}_{a,k}\), which they call double Danielewski surfaces [N. Gupta and S. Sen, J. Algebra 533, 25–43 (2019; Zbl 1437.14064)]. For such surfaces which admit a unique equivalence class of \(\mathbb{G}_{a,k}\)-actions, in the sense that all actions have the same ring of invariants, they determine explicit expressions for all possible locally nilpotent derivations of their coordinate rings.
References:
| [1] | Daigle, D., On locally nilpotent derivations of \(k [x_1, x_2, y] /(\phi(y) - x_1 x_2)\), J. Pure Appl. Algebra, 181, 181-208 (2003) · Zbl 1077.13013 |
| [2] | Gupta, N.; Sen, S., On double Danielewski surfaces and the cancellation problem, J. Algebra, 533, 25-43 (2019) · Zbl 1437.14064 |
| [3] | Makar-Limanov, L., On the group of automorphisms of a surface \(x^n y = p(z)\), Isr. J. Math., 121, 113-123 (2001) · Zbl 0980.14030 |
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