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arXiv · 1907.13259

On the rigidity of certain Pham-Brieskorn rings

Michael Chitayat·Daniel Daigle
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Abstract

Fix a field $k$ of characteristic zero. If $a_1, ..., a_n$ ($n>2$) are positive integers, the integral domain $B = k[X_1, ..., X_n] / ( X_1^{a_1} + ... + X_n^{a_n} )$ is called a Pham-Brieskorn ring. It is conjectured that if $a_i > 1$ for all $i$ and $a_i=2$ for at most one $i$, then $B$ is rigid. (A ring $B$ is said to be rigid if the only locally nilpotent derivation $D: B \to B$ is the zero derivation.) We give partial results towards the conjecture.

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Michael Chitayat, Daniel Daigle. 2019-07-30. On the rigidity of certain Pham-Brieskorn rings. https://arxiv.org/abs/1907.13259

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