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arXiv · 2509.07490

A new proof of non-Cohen-Macaulayness of Bertin's example

Takuma Seno
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Abstract

Bertin's example is famous as the first known Noetherian UFD that is not Cohen-Macaulay. In the example, she employed a ring of invariants and proved that the ring is not Cohen-Macaulay by calculating a homogeneous system of parameter and generators of it. In this paper, we give a new proof by arguments on ring theoretic properties.

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Takuma Seno. 2025-09-09. A new proof of non-Cohen-Macaulayness of Bertin's example. https://arxiv.org/abs/2509.07490

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