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arXiv · 2312.07587

The Rigid Pham-Brieskorn Threefolds

Michael Chitayat·Adrien Dubouloz
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Abstract

We show that a $3$-dimensional Pham-Brieskorn hypersurface $\{ X_0^{a_0} + X_1^{a_1} + X_2^{a_2} + X_3^{a_3}=0\}$ in $\mathbb{A}^4$ such that $\min\{a_0, a_1, a_2, a_3 \} \geq 2$ and at most one element $i$ of $\{0,1,2,3\}$ satisfies $a_i = 2$ does not admit a non-trivial action of the additive group $\mathbb{G}_a$.

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Michael Chitayat, Adrien Dubouloz. 2023-12-11. The Rigid Pham-Brieskorn Threefolds. https://arxiv.org/abs/2312.07587

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