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On the hypersurface \(x+x^2y+z^2+t^3=0\) in \(\mathbb{C}^4\) or a \(\mathbb{C}^3\)-like threefold which is not \(\mathbb{C}^3\). (English) Zbl 0896.14021
In this note the author proves that the threefold in \(\mathbb{C}^4\) which is given by \(x+x^2y+ z^2+t^3=0\) is not isomorphic to \(\mathbb{C}^3\). The proof uses locally nilpotent derivations on rings. The problem is related with the linearizing conjecture for the actions of \(\mathbb{C}^*\) on \(\mathbb{C}^3\).

MSC:
14J30 \(3\)-folds
14L30 Group actions on varieties or schemes (quotients)
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