G-stable rank of symmetric tensors and log canonical threshold

Zhi Jiang

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arXiv · 2203.03527

G-stable rank of symmetric tensors and log canonical threshold

Zhi Jiang

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Abstract

Shitov recently gave a counterexample to Comon's conjecture that the symmetric tensor rank and tensor rank of a symmetric tensor are the same. In this paper we show that an analog of Comon's conjecture for the G-stable rank introduced by Derksen is true: the symmetric G-stable rank and G-stable rank of a symmetric tensor are the same. We also show that the log-canonical threshold of a singularity is bounded by the G-stable rank of the defining ideal.

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Zhi Jiang. 2022-03-07. G-stable rank of symmetric tensors and log canonical threshold. https://arxiv.org/abs/2203.03527

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