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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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##### References:
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